Neutron computed tomography(NCT)is widely used as a noninvasive measurement technique in nuclear engineering,thermal hydraulics,and cultural heritage.The neutron source intensity of NCT is usually low and the scan tim...Neutron computed tomography(NCT)is widely used as a noninvasive measurement technique in nuclear engineering,thermal hydraulics,and cultural heritage.The neutron source intensity of NCT is usually low and the scan time is long,resulting in a projection image containing severe noise.To reduce the scanning time and increase the image reconstruction quality,an effective reconstruction algorithm must be selected.In CT image reconstruction,the reconstruction algorithms can be divided into three categories:analytical algorithms,iterative algorithms,and deep learning.Because the analytical algorithm requires complete projection data,it is not suitable for reconstruction in harsh environments,such as strong radia-tion,high temperature,and high pressure.Deep learning requires large amounts of data and complex models,which cannot be easily deployed,as well as has a high computational complexity and poor interpretability.Therefore,this paper proposes the OS-SART-PDTV iterative algorithm,which uses the ordered subset simultaneous algebraic reconstruction technique(OS-SART)algorithm to reconstruct the image and the first-order primal–dual algorithm to solve the total variation(PDTV),for sparse-view NCT three-dimensional reconstruction.The novel algorithm was compared with other algorithms(FBP,OS-SART-TV,OS-SART-AwTV,and OS-SART-FGPTV)by simulating the experimental data and actual neutron projection experiments.The reconstruction results demonstrate that the proposed algorithm outperforms the FBP,OS-SART-TV,OS-SART-AwTV,and OS-SART-FGPTV algorithms in terms of preserving edge structure,denoising,and suppressing artifacts.展开更多
The distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of n local cost functions by using local information exchange is considered.This problem is an important component of...The distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of n local cost functions by using local information exchange is considered.This problem is an important component of many machine learning techniques with data parallelism,such as deep learning and federated learning.We propose a distributed primal-dual stochastic gradient descent(SGD)algorithm,suitable for arbitrarily connected communication networks and any smooth(possibly nonconvex)cost functions.We show that the proposed algorithm achieves the linear speedup convergence rate O(1/(√nT))for general nonconvex cost functions and the linear speedup convergence rate O(1/(nT)) when the global cost function satisfies the Polyak-Lojasiewicz(P-L)condition,where T is the total number of iterations.We also show that the output of the proposed algorithm with constant parameters linearly converges to a neighborhood of a global optimum.We demonstrate through numerical experiments the efficiency of our algorithm in comparison with the baseline centralized SGD and recently proposed distributed SGD algorithms.展开更多
Two existing methods for solving a class of fuzzy linear programming (FLP) problems involving symmetric trapezoidal fuzzy numbers without converting them to crisp linear programming problems are the fuzzy primal simpl...Two existing methods for solving a class of fuzzy linear programming (FLP) problems involving symmetric trapezoidal fuzzy numbers without converting them to crisp linear programming problems are the fuzzy primal simplex method proposed by Ganesan and Veeramani [1] and the fuzzy dual simplex method proposed by Ebrahimnejad and Nasseri [2]. The former method is not applicable when a primal basic feasible solution is not easily at hand and the later method needs to an initial dual basic feasible solution. In this paper, we develop a novel approach namely the primal-dual simplex algorithm to overcome mentioned shortcomings. A numerical example is given to illustrate the proposed approach.展开更多
Long-term responses of floating structures pose a great concern in their design phase. Existing approaches for addressing long-term extreme responses are extremely cumbersome for adoption. This work aims to develop an...Long-term responses of floating structures pose a great concern in their design phase. Existing approaches for addressing long-term extreme responses are extremely cumbersome for adoption. This work aims to develop an approach for the long-term extreme-response analysis of floating structures. A modified gradient-based retrieval algorithm in conjunction with the inverse first-order reliability method(IFORM) is proposed to enable the use of convolution models in long-term extreme analysis of structures with an analytical formula of response amplitude operator(RAO). The proposed algorithm ensures convergence stability and iteration accuracy and exhibits a higher computational efficiency than the traditional backtracking method. However, when the RAO of general offshore structures cannot be analytically expressed, the convolutional integration method fails to function properly. A numerical discretization approach is further proposed for offshore structures in the case when the analytical expression of the RAO is not feasible. Through iterative discretization of environmental contours(ECs) and RAOs, a detailed procedure is proposed to calculate the long-term response extremes of offshore structures. The validity and accuracy of the proposed approach are tested using a floating offshore wind turbine as a numerical example. The long-term extreme heave responses of various return periods are calculated via the IFORM in conjunction with a numerical discretization approach. The environmental data corresponding to N-year structural responses are located inside the ECs, which indicates that the selection of design points directly along the ECs yields conservative design results.展开更多
In order to address the complex uncertainties caused by interfacing between the fuzziness and randomness of the safety problem for embankment engineering projects, and to evaluate the safety of embankment engineering ...In order to address the complex uncertainties caused by interfacing between the fuzziness and randomness of the safety problem for embankment engineering projects, and to evaluate the safety of embankment engineering projects more scientifically and reasonably, this study presents the fuzzy logic modeling of the stochastic finite element method （SFEM） based on the harmonious finite element （HFE） technique using a first-order approximation theorem. Fuzzy mathematical models of safety repertories were introduced into the SFEM to analyze the stability of embankments and foundations in order to describe the fuzzy failure procedure for the random safety performance function. The fuzzy models were developed with membership functions with half depressed gamma distribution, half depressed normal distribution, and half depressed echelon distribution. The fuzzy stochastic mathematical algorithm was used to comprehensively study the local failure mechanism of the main embankment section near Jingnan in the Yangtze River in terms of numerical analysis for the probability integration of reliability on the random field affected by three fuzzy factors. The result shows that the middle region of the embankment is the principal zone of concentrated failure due to local fractures. There is also some local shear failure on the embankment crust. This study provides a referential method for solving complex multi-uncertainty problems in engineering safety analysis.展开更多
In this paper, we propose a primal-dual interior point method for solving general constrained nonlinear programming problems. To avoid the situation that the algorithm we use may converge to a saddle point or a local ...In this paper, we propose a primal-dual interior point method for solving general constrained nonlinear programming problems. To avoid the situation that the algorithm we use may converge to a saddle point or a local maximum, we utilize a merit function to guide the iterates toward a local minimum. Especially, we add the parameter ε to the Newton system when calculating the decrease directions. The global convergence is achieved by the decrease of a merit function. Furthermore, the numerical results confirm that the algorithm can solve this kind of problems in an efficient way.展开更多
Two new versions of accelerated first-order methods for minimizing convex composite functions are proposed. In this paper, we first present an accelerated first-order method which chooses the step size 1/ Lk to be 1/ ...Two new versions of accelerated first-order methods for minimizing convex composite functions are proposed. In this paper, we first present an accelerated first-order method which chooses the step size 1/ Lk to be 1/ L0 at the beginning of each iteration and preserves the computational simplicity of the fast iterative shrinkage-thresholding algorithm. The first proposed algorithm is a non-monotone algorithm. To avoid this behavior, we present another accelerated monotone first-order method. The proposed two accelerated first-order methods are proved to have a better convergence rate for minimizing convex composite functions. Numerical results demonstrate the efficiency of the proposed two accelerated first-order methods.展开更多
Interior-point methods （IPMs） for linear optimization （LO） and semidefinite optimization （SDO） have become a hot area in mathematical programming in the last decades. In this paper, a new kernel function with si...Interior-point methods （IPMs） for linear optimization （LO） and semidefinite optimization （SDO） have become a hot area in mathematical programming in the last decades. In this paper, a new kernel function with simple algebraic expression is proposed. Based on this kernel function, a primal-dual interior-point methods （IPMs） for semidefinite optimization （SDO） is designed. And the iteration complexity of the algorithm as O（n^3/4 log n/ε） with large-updates is established. The resulting bound is better than the classical kernel function, with its iteration complexity O（n log n/ε） in large-updates case.展开更多
develop a mentation This paper considers the priority facility primal-dual 3-approximation algorithm for procedure, the authors further improve the location problem with penalties： The authors this problem. Combining...develop a mentation This paper considers the priority facility primal-dual 3-approximation algorithm for procedure, the authors further improve the location problem with penalties： The authors this problem. Combining with the greedy aug- previous ratio 3 to 1.8526.展开更多
Nonlinear convex cone programming(NCCP)models have found many practical applications.In this paper,we introduce a flexible first-order primal-dual algorithm,called the variant auxiliary problem principle(VAPP),for sol...Nonlinear convex cone programming(NCCP)models have found many practical applications.In this paper,we introduce a flexible first-order primal-dual algorithm,called the variant auxiliary problem principle(VAPP),for solving NCCP problems when the objective function and constraints are convex but may be nonsmooth.At each iteration,VAPP generates a nonlinear approximation of the primal augmented Lagrangian model.The approximation incorporates both linearization and a distance-like proximal term,and then the iterations of VAPP are shown to possess a decomposition property for NCCP.Motivated by recent applications in big data analytics,there has been a growing interest in the convergence rate analysis of algorithms with parallel computing capabilities for large scale optimization problems.We establish O(1/t)convergence rate towards primal optimality,feasibility and dual optimality.By adaptively setting parameters at different iterations,we show an O(1/t2)rate for the strongly convex case.Finally,we discuss some issues in the implementation of VAPP.展开更多
In this paper,we consider a block-structured convex optimization model,where in the objective the block variables are nonseparable and they are further linearly coupled in the constraint.For the 2-block case,we propos...In this paper,we consider a block-structured convex optimization model,where in the objective the block variables are nonseparable and they are further linearly coupled in the constraint.For the 2-block case,we propose a number of first-order algorithms to solve this model.First,the alternating direction method of multipliers(ADMM)is extended,assuming that it is easy to optimize the augmented Lagrangian function with one block of variables at each time while fixing the other block.We prove that O(1/t)iteration complexity bound holds under suitable conditions,where t is the number of iterations.If the subroutines of the ADMM cannot be implemented,then we propose new alternative algorithms to be called alternating proximal gradient method of multipliers,alternating gradient projection method of multipliers,and the hybrids thereof.Under suitable conditions,the O(1/t)iteration complexity bound is shown to hold for all the newly proposed algorithms.Finally,we extend the analysis for the ADMM to the general multi-block case.展开更多
In this paper,we consider the generalized prize-collecting Steiner forest problem,extending the prize-collecting Steiner forest problem.In this problem,we are given a connected graph G=(V,E)and a set of vertex sets V=...In this paper,we consider the generalized prize-collecting Steiner forest problem,extending the prize-collecting Steiner forest problem.In this problem,we are given a connected graph G=(V,E)and a set of vertex sets V={V1,V2,…,Vl}.Every edge in E has a nonnegative cost,and every vertex set in V has a nonnegative penalty cost.For a given edge set F⊆E,vertex set Vi∈V is said to be connected by edge set F if Vi is in a connected component of the F-spanned subgraph.The objective is to find such an edge set F such that the total edge cost in F and the penalty cost of the vertex sets not connected by F is minimized.Our main contribution is to give a 3-approximation algorithm for this problem via the primal-dual method.展开更多
In this paper,we consider the-prize-collecting minimum vertex cover problem with submodular penalties,which generalizes the well-known minimum vertex cover problem,minimum partial vertex cover problem and minimum vert...In this paper,we consider the-prize-collecting minimum vertex cover problem with submodular penalties,which generalizes the well-known minimum vertex cover problem,minimum partial vertex cover problem and minimum vertex cover problem with submodular penalties.We are given a cost graph and an integer.This problem determines a vertex set such that covers at least edges.The objective is to minimize the total cost of the vertices in plus the penalty of the uncovered edge set,where the penalty is determined by a submodular function.We design a two-phase combinatorial algorithm based on the guessing technique and the primal-dual framework to address the problem.When the submodular penalty cost function is normalized and nondecreasing,the proposed algorithm has an approximation factor of.When the submodular penalty cost function is linear,the approximation factor of the proposed algorithm is reduced to,which is the best factor if the unique game conjecture holds.展开更多
We have proposed a primal-dual fixed point algorithm （PDFP） for solving minimiza- tion of the sum of three convex separable functions, which involves a smooth function with Lipschitz continuous gradient, a linear co...We have proposed a primal-dual fixed point algorithm （PDFP） for solving minimiza- tion of the sum of three convex separable functions, which involves a smooth function with Lipschitz continuous gradient, a linear composite nonsmooth function, and a nonsmooth function. Compared with similar works, the parameters in PDFP are easier to choose and are allowed in a relatively larger range. We will extend PDFP to solve two kinds of separable multi-block minimization problems, arising in signal processing and imaging science. This work shows the flexibility of applying PDFP algorithm to multi-block prob- lems and illustrates how practical and fully splitting schemes can be derived, especially for parallel implementation of large scale problems. The connections and comparisons to the alternating direction method of multiplier （ADMM） are also present. We demonstrate how different algorithms can be obtained by splitting the problems in different ways through the classic example of sparsity regularized least square model with constraint. In particular, for a class of linearly constrained problems, which are of great interest in the context of multi-block ADMM, can be also solved by PDFP with a guarantee of convergence. Finally, some experiments are provided to illustrate the performance of several schemes derived by the PDFP algorithm.展开更多
To meet the high demand for reliability based design of slopes, we present in this paper a simplified HLRF(Hasofere Linde Rackwitze Fiessler) iterative algorithm for first-order reliability method(FORM). It is simply ...To meet the high demand for reliability based design of slopes, we present in this paper a simplified HLRF(Hasofere Linde Rackwitze Fiessler) iterative algorithm for first-order reliability method(FORM). It is simply formulated in x-space and requires neither transformation of correlated random variables nor optimization tools. The solution can be easily improved by iteratively adjusting the step length. The algorithm is particularly useful to practicing engineers for geotechnical reliability analysis where standalone(deterministic) numerical packages are used. Based on the proposed algorithm and through direct perturbation analysis of random variables, we conducted a case study of earth slope reliability with complete consideration of soil uncertainty and spatial variability.展开更多
This paper presents a reliability analysis of the pseudo-static seismic bearing capacity of a strip foundation using the limit equilibrium theory. The first-order reliability method(FORM) is employed to calculate the ...This paper presents a reliability analysis of the pseudo-static seismic bearing capacity of a strip foundation using the limit equilibrium theory. The first-order reliability method(FORM) is employed to calculate the reliability index. The response surface methodology(RSM) is used to assess the Hasofer e Lind reliability index and then it is optimized using a genetic algorithm(GA). The random variables used are the soil shear strength parameters and the seismic coefficients(khand kv). Two assumptions(normal and non-normal distribution) are used for the random variables. The assumption of uncorrelated variables was found to be conservative in comparison to that of negatively correlated soil shear strength parameters. The assumption of non-normal distribution for the random variables can induce a negative effect on the reliability index of the practical range of the seismic bearing capacity.展开更多
In this paper,we consider an optimization problem of the grasping manipulation of multi-fingered hand-arm robots.We first formulate an optimization model for the problem,based on the dynamic equations of the object a...In this paper,we consider an optimization problem of the grasping manipulation of multi-fingered hand-arm robots.We first formulate an optimization model for the problem,based on the dynamic equations of the object and the friction constraints.Then,we reformulate the model as a convex quadratic programming over circular cones.Moreover,we propose a primal-dual interior-point algorithm based on the kernel function to solve this convex quadratic programming over circular cones.We derive both the convergence of the algorithm and the iteration bounds for largeand small-update methods,respectively.Finally,we carry out the numerical tests of 180◦and 90◦manipulations of the hand-arm robot to demonstrate the effectiveness of the proposed algorithm.展开更多
基金supported by the National Key Research and Development Program of China(No.2022YFB1902700)the Joint Fund of Ministry of Education for Equipment Pre-research(No.8091B042203)+5 种基金the National Natural Science Foundation of China(No.11875129)the Fund of the State Key Laboratory of Intense Pulsed Radiation Simulation and Effect(No.SKLIPR1810)the Fund of Innovation Center of Radiation Application(No.KFZC2020020402)the Fund of the State Key Laboratory of Nuclear Physics and Technology,Peking University(No.NPT2023KFY06)the Joint Innovation Fund of China National Uranium Co.,Ltd.,State Key Laboratory of Nuclear Resources and Environment,East China University of Technology(No.2022NRE-LH-02)the Fundamental Research Funds for the Central Universities(No.2023JG001).
文摘Neutron computed tomography(NCT)is widely used as a noninvasive measurement technique in nuclear engineering,thermal hydraulics,and cultural heritage.The neutron source intensity of NCT is usually low and the scan time is long,resulting in a projection image containing severe noise.To reduce the scanning time and increase the image reconstruction quality,an effective reconstruction algorithm must be selected.In CT image reconstruction,the reconstruction algorithms can be divided into three categories:analytical algorithms,iterative algorithms,and deep learning.Because the analytical algorithm requires complete projection data,it is not suitable for reconstruction in harsh environments,such as strong radia-tion,high temperature,and high pressure.Deep learning requires large amounts of data and complex models,which cannot be easily deployed,as well as has a high computational complexity and poor interpretability.Therefore,this paper proposes the OS-SART-PDTV iterative algorithm,which uses the ordered subset simultaneous algebraic reconstruction technique(OS-SART)algorithm to reconstruct the image and the first-order primal–dual algorithm to solve the total variation(PDTV),for sparse-view NCT three-dimensional reconstruction.The novel algorithm was compared with other algorithms(FBP,OS-SART-TV,OS-SART-AwTV,and OS-SART-FGPTV)by simulating the experimental data and actual neutron projection experiments.The reconstruction results demonstrate that the proposed algorithm outperforms the FBP,OS-SART-TV,OS-SART-AwTV,and OS-SART-FGPTV algorithms in terms of preserving edge structure,denoising,and suppressing artifacts.
基金supported by the Knut and Alice Wallenberg Foundationthe Swedish Foundation for Strategic Research+1 种基金the Swedish Research Councilthe National Natural Science Foundation of China(62133003,61991403,61991404,61991400)。
文摘The distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of n local cost functions by using local information exchange is considered.This problem is an important component of many machine learning techniques with data parallelism,such as deep learning and federated learning.We propose a distributed primal-dual stochastic gradient descent(SGD)algorithm,suitable for arbitrarily connected communication networks and any smooth(possibly nonconvex)cost functions.We show that the proposed algorithm achieves the linear speedup convergence rate O(1/(√nT))for general nonconvex cost functions and the linear speedup convergence rate O(1/(nT)) when the global cost function satisfies the Polyak-Lojasiewicz(P-L)condition,where T is the total number of iterations.We also show that the output of the proposed algorithm with constant parameters linearly converges to a neighborhood of a global optimum.We demonstrate through numerical experiments the efficiency of our algorithm in comparison with the baseline centralized SGD and recently proposed distributed SGD algorithms.
文摘Two existing methods for solving a class of fuzzy linear programming (FLP) problems involving symmetric trapezoidal fuzzy numbers without converting them to crisp linear programming problems are the fuzzy primal simplex method proposed by Ganesan and Veeramani [1] and the fuzzy dual simplex method proposed by Ebrahimnejad and Nasseri [2]. The former method is not applicable when a primal basic feasible solution is not easily at hand and the later method needs to an initial dual basic feasible solution. In this paper, we develop a novel approach namely the primal-dual simplex algorithm to overcome mentioned shortcomings. A numerical example is given to illustrate the proposed approach.
基金Supported by the National Natural Science Foundation of China (Grant Nos.52088102 and 51879287)National Key Research and Development Program of China (Grant No.2022YFB2602301)。
文摘Long-term responses of floating structures pose a great concern in their design phase. Existing approaches for addressing long-term extreme responses are extremely cumbersome for adoption. This work aims to develop an approach for the long-term extreme-response analysis of floating structures. A modified gradient-based retrieval algorithm in conjunction with the inverse first-order reliability method(IFORM) is proposed to enable the use of convolution models in long-term extreme analysis of structures with an analytical formula of response amplitude operator(RAO). The proposed algorithm ensures convergence stability and iteration accuracy and exhibits a higher computational efficiency than the traditional backtracking method. However, when the RAO of general offshore structures cannot be analytically expressed, the convolutional integration method fails to function properly. A numerical discretization approach is further proposed for offshore structures in the case when the analytical expression of the RAO is not feasible. Through iterative discretization of environmental contours(ECs) and RAOs, a detailed procedure is proposed to calculate the long-term response extremes of offshore structures. The validity and accuracy of the proposed approach are tested using a floating offshore wind turbine as a numerical example. The long-term extreme heave responses of various return periods are calculated via the IFORM in conjunction with a numerical discretization approach. The environmental data corresponding to N-year structural responses are located inside the ECs, which indicates that the selection of design points directly along the ECs yields conservative design results.
基金supported by the National Natural Science Foundation of China(Grant No.50379046)the Doctoral Fund of the Ministry of Education of China(Grant No.A50221)
文摘In order to address the complex uncertainties caused by interfacing between the fuzziness and randomness of the safety problem for embankment engineering projects, and to evaluate the safety of embankment engineering projects more scientifically and reasonably, this study presents the fuzzy logic modeling of the stochastic finite element method （SFEM） based on the harmonious finite element （HFE） technique using a first-order approximation theorem. Fuzzy mathematical models of safety repertories were introduced into the SFEM to analyze the stability of embankments and foundations in order to describe the fuzzy failure procedure for the random safety performance function. The fuzzy models were developed with membership functions with half depressed gamma distribution, half depressed normal distribution, and half depressed echelon distribution. The fuzzy stochastic mathematical algorithm was used to comprehensively study the local failure mechanism of the main embankment section near Jingnan in the Yangtze River in terms of numerical analysis for the probability integration of reliability on the random field affected by three fuzzy factors. The result shows that the middle region of the embankment is the principal zone of concentrated failure due to local fractures. There is also some local shear failure on the embankment crust. This study provides a referential method for solving complex multi-uncertainty problems in engineering safety analysis.
文摘In this paper, we propose a primal-dual interior point method for solving general constrained nonlinear programming problems. To avoid the situation that the algorithm we use may converge to a saddle point or a local maximum, we utilize a merit function to guide the iterates toward a local minimum. Especially, we add the parameter ε to the Newton system when calculating the decrease directions. The global convergence is achieved by the decrease of a merit function. Furthermore, the numerical results confirm that the algorithm can solve this kind of problems in an efficient way.
基金Sponsored by the National Natural Science Foundation of China(Grant No.11461021)the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2017JM1014)
文摘Two new versions of accelerated first-order methods for minimizing convex composite functions are proposed. In this paper, we first present an accelerated first-order method which chooses the step size 1/ Lk to be 1/ L0 at the beginning of each iteration and preserves the computational simplicity of the fast iterative shrinkage-thresholding algorithm. The first proposed algorithm is a non-monotone algorithm. To avoid this behavior, we present another accelerated monotone first-order method. The proposed two accelerated first-order methods are proved to have a better convergence rate for minimizing convex composite functions. Numerical results demonstrate the efficiency of the proposed two accelerated first-order methods.
基金Project supported by the National Natural Science Foundation of China （Grant No. 10117733）, the Shanghai Leading Academic Discipline Project （Grant No.J50101）, and the Foundation of Scientific Research for Selecting and Cultivating Young Excellent University Teachers in Shanghai （Grant No.06XPYQ52）
文摘Interior-point methods （IPMs） for linear optimization （LO） and semidefinite optimization （SDO） have become a hot area in mathematical programming in the last decades. In this paper, a new kernel function with simple algebraic expression is proposed. Based on this kernel function, a primal-dual interior-point methods （IPMs） for semidefinite optimization （SDO） is designed. And the iteration complexity of the algorithm as O（n^3/4 log n/ε） with large-updates is established. The resulting bound is better than the classical kernel function, with its iteration complexity O（n log n/ε） in large-updates case.
基金supported by the National Natural Science Foundation of China under Grant No.11371001
文摘develop a mentation This paper considers the priority facility primal-dual 3-approximation algorithm for procedure, the authors further improve the location problem with penalties： The authors this problem. Combining with the greedy aug- previous ratio 3 to 1.8526.
基金This research was supported by the National Natural Science Foundation of China(Nos.71471112 and 71871140).
文摘Nonlinear convex cone programming(NCCP)models have found many practical applications.In this paper,we introduce a flexible first-order primal-dual algorithm,called the variant auxiliary problem principle(VAPP),for solving NCCP problems when the objective function and constraints are convex but may be nonsmooth.At each iteration,VAPP generates a nonlinear approximation of the primal augmented Lagrangian model.The approximation incorporates both linearization and a distance-like proximal term,and then the iterations of VAPP are shown to possess a decomposition property for NCCP.Motivated by recent applications in big data analytics,there has been a growing interest in the convergence rate analysis of algorithms with parallel computing capabilities for large scale optimization problems.We establish O(1/t)convergence rate towards primal optimality,feasibility and dual optimality.By adaptively setting parameters at different iterations,we show an O(1/t2)rate for the strongly convex case.Finally,we discuss some issues in the implementation of VAPP.
文摘In this paper,we consider a block-structured convex optimization model,where in the objective the block variables are nonseparable and they are further linearly coupled in the constraint.For the 2-block case,we propose a number of first-order algorithms to solve this model.First,the alternating direction method of multipliers(ADMM)is extended,assuming that it is easy to optimize the augmented Lagrangian function with one block of variables at each time while fixing the other block.We prove that O(1/t)iteration complexity bound holds under suitable conditions,where t is the number of iterations.If the subroutines of the ADMM cannot be implemented,then we propose new alternative algorithms to be called alternating proximal gradient method of multipliers,alternating gradient projection method of multipliers,and the hybrids thereof.Under suitable conditions,the O(1/t)iteration complexity bound is shown to hold for all the newly proposed algorithms.Finally,we extend the analysis for the ADMM to the general multi-block case.
基金the National Natural Science Foundation of China(No.11371001)Collaborative Innovation Center on Beijing Society-Building and Social Governance.D.-L.Du is supported by the Natural Sciences and Engineering Research Council of Canada(No.06446).C.-C.Wu is supported by the National Natural Science Foundation of China(No.11501412).
文摘In this paper,we consider the generalized prize-collecting Steiner forest problem,extending the prize-collecting Steiner forest problem.In this problem,we are given a connected graph G=(V,E)and a set of vertex sets V={V1,V2,…,Vl}.Every edge in E has a nonnegative cost,and every vertex set in V has a nonnegative penalty cost.For a given edge set F⊆E,vertex set Vi∈V is said to be connected by edge set F if Vi is in a connected component of the F-spanned subgraph.The objective is to find such an edge set F such that the total edge cost in F and the penalty cost of the vertex sets not connected by F is minimized.Our main contribution is to give a 3-approximation algorithm for this problem via the primal-dual method.
基金The work was supported in part by the National Natural Science Foundation of China(Grant No.12071417)。
文摘In this paper,we consider the-prize-collecting minimum vertex cover problem with submodular penalties,which generalizes the well-known minimum vertex cover problem,minimum partial vertex cover problem and minimum vertex cover problem with submodular penalties.We are given a cost graph and an integer.This problem determines a vertex set such that covers at least edges.The objective is to minimize the total cost of the vertices in plus the penalty of the uncovered edge set,where the penalty is determined by a submodular function.We design a two-phase combinatorial algorithm based on the guessing technique and the primal-dual framework to address the problem.When the submodular penalty cost function is normalized and nondecreasing,the proposed algorithm has an approximation factor of.When the submodular penalty cost function is linear,the approximation factor of the proposed algorithm is reduced to,which is the best factor if the unique game conjecture holds.
文摘We have proposed a primal-dual fixed point algorithm （PDFP） for solving minimiza- tion of the sum of three convex separable functions, which involves a smooth function with Lipschitz continuous gradient, a linear composite nonsmooth function, and a nonsmooth function. Compared with similar works, the parameters in PDFP are easier to choose and are allowed in a relatively larger range. We will extend PDFP to solve two kinds of separable multi-block minimization problems, arising in signal processing and imaging science. This work shows the flexibility of applying PDFP algorithm to multi-block prob- lems and illustrates how practical and fully splitting schemes can be derived, especially for parallel implementation of large scale problems. The connections and comparisons to the alternating direction method of multiplier （ADMM） are also present. We demonstrate how different algorithms can be obtained by splitting the problems in different ways through the classic example of sparsity regularized least square model with constraint. In particular, for a class of linearly constrained problems, which are of great interest in the context of multi-block ADMM, can be also solved by PDFP with a guarantee of convergence. Finally, some experiments are provided to illustrate the performance of several schemes derived by the PDFP algorithm.
基金Financial supports from National Science Foundation of China(Grant Nos.51609072,51879091,51479050 and 41630638)the National Key Basic Research Program of China("973" Program)(Grant No.2015CB057901)the Public Service Sector R&D Project of Ministry of Water Resource of China(Grant No.201501035-03)
文摘To meet the high demand for reliability based design of slopes, we present in this paper a simplified HLRF(Hasofere Linde Rackwitze Fiessler) iterative algorithm for first-order reliability method(FORM). It is simply formulated in x-space and requires neither transformation of correlated random variables nor optimization tools. The solution can be easily improved by iteratively adjusting the step length. The algorithm is particularly useful to practicing engineers for geotechnical reliability analysis where standalone(deterministic) numerical packages are used. Based on the proposed algorithm and through direct perturbation analysis of random variables, we conducted a case study of earth slope reliability with complete consideration of soil uncertainty and spatial variability.
基金the Ministry of Higher Education and Scientific Research of Algeria for supporting this work by offering an 11-month scholarship to the first author at the 3SR laboratory of Grenoble Alpes University,France
文摘This paper presents a reliability analysis of the pseudo-static seismic bearing capacity of a strip foundation using the limit equilibrium theory. The first-order reliability method(FORM) is employed to calculate the reliability index. The response surface methodology(RSM) is used to assess the Hasofer e Lind reliability index and then it is optimized using a genetic algorithm(GA). The random variables used are the soil shear strength parameters and the seismic coefficients(khand kv). Two assumptions(normal and non-normal distribution) are used for the random variables. The assumption of uncorrelated variables was found to be conservative in comparison to that of negatively correlated soil shear strength parameters. The assumption of non-normal distribution for the random variables can induce a negative effect on the reliability index of the practical range of the seismic bearing capacity.
基金the National Natural Science Foundation of China(No.11371242)。
文摘In this paper,we consider an optimization problem of the grasping manipulation of multi-fingered hand-arm robots.We first formulate an optimization model for the problem,based on the dynamic equations of the object and the friction constraints.Then,we reformulate the model as a convex quadratic programming over circular cones.Moreover,we propose a primal-dual interior-point algorithm based on the kernel function to solve this convex quadratic programming over circular cones.We derive both the convergence of the algorithm and the iteration bounds for largeand small-update methods,respectively.Finally,we carry out the numerical tests of 180◦and 90◦manipulations of the hand-arm robot to demonstrate the effectiveness of the proposed algorithm.
