To preserve the edges and details of the image,a new variational model for wavelet domain inpainting was proposed which contained a non-convex regularizer. The non-convex regularizer can utilize the local information ...To preserve the edges and details of the image,a new variational model for wavelet domain inpainting was proposed which contained a non-convex regularizer. The non-convex regularizer can utilize the local information of image and perform better than those usual convex ones. In addition, to solve the non-convex minimization problem,an iterative reweighted method and a primaldual method were designed. The numerical experiments show that the new model not only gets better visual effects but also obtains higher signal to noise ratio than the recent method.展开更多
In the present paper we present a class of polynomial primal-dual interior-point algorithms for semidefmite optimization based on a kernel function. This kernel function is not a so-called self-regular function due to...In the present paper we present a class of polynomial primal-dual interior-point algorithms for semidefmite optimization based on a kernel function. This kernel function is not a so-called self-regular function due to its growth term increasing linearly. Some new analysis tools were developed which can be used to deal with complexity ＂analysis of the algorithms which use analogous strategy in [5] to design the search directions for the Newton system. The complexity bounds for the algorithms with large- and small-update methodswere obtained, namely,O（qn^（p＋q/q（P＋1）log n/ε and O（q^2√n）log n/ε,respectlvely.展开更多
This paper proposes an infeasible interior-point algorithm for linear complementarity problem with full-Newton steps.The main iteration consists of a feasibility step and several centrality steps.No more than O（n log...This paper proposes an infeasible interior-point algorithm for linear complementarity problem with full-Newton steps.The main iteration consists of a feasibility step and several centrality steps.No more than O（n log（n /ε））iterations are required for getting ε-solution of the problem at hand,which coincides with the best-known bound for infeasible interior-point algorithms.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
We present a primal-dual discontinuous Galerkin finite element method for a type of ill-posed elliptic Cauchy problem.It is shown that the discrete problem attains a unique solution,if the solution of the ill-posed el...We present a primal-dual discontinuous Galerkin finite element method for a type of ill-posed elliptic Cauchy problem.It is shown that the discrete problem attains a unique solution,if the solution of the ill-posed elliptic Cauchy problems is unique.An optimal error estimate is obtained in a H1-like norm.Numerical experiments are provided to demonstrate the efficiency of the proposed method.展开更多
Kernel functions play an important role in defining new search directions for primal-dual interior-point algorithm for solving linear optimization problems. In this paper we present a new kernel function which yields ...Kernel functions play an important role in defining new search directions for primal-dual interior-point algorithm for solving linear optimization problems. In this paper we present a new kernel function which yields an algorithm with the best known complexity bound for both large- and small-update methods.展开更多
We consider the problem of restoring images corrupted by Poisson noise. Under the framework of maximum a posteriori estimator, the problem can be converted into a minimization problem where the objective function is c...We consider the problem of restoring images corrupted by Poisson noise. Under the framework of maximum a posteriori estimator, the problem can be converted into a minimization problem where the objective function is composed of a Kullback-Leibler(KL)-divergence term for the Poisson noise and a total variation(TV) regularization term. Due to the logarithm function in the KL-divergence term, the non-differentiability of TV term and the positivity constraint on the images, it is not easy to design stable and efficiency algorithm for the problem. Recently, many researchers proposed to solve the problem by alternating direction method of multipliers(ADMM). Since the approach introduces some auxiliary variables and requires the solution of some linear systems, the iterative procedure can be complicated. Here we formulate the problem as two new constrained minimax problems and solve them by Chambolle-Pock's first order primal-dual approach. The convergence of our approach is guaranteed by their theory. Comparing with ADMM approaches, our approach requires about half of the auxiliary variables and is matrix-inversion free. Numerical results show that our proposed algorithms are efficient and outperform the ADMM approach.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
In this paper,an integrated guidance and control approach is presented to improve the performance of the missile interception.The approach includes damping augmented system with attitude rate feedback to decrease the ...In this paper,an integrated guidance and control approach is presented to improve the performance of the missile interception.The approach includes damping augmented system with attitude rate feedback to decrease the oscillation during the homing phase for missiles with low damping.In addition,physical constraints,which can affect the performance of the missile interception,such as acceleration limit,seeker’s look angle,and look angle rate constraints are considered.The integrated guidance and control problem is formulated as a convex quadratic optimization problem with equality and inequality constraints,and the solution is obtained by a primal–dual interior point method.The performance of the proposed method is verified through several numerical examples.展开更多
In this paper,we develop a distributed solver for a group of strict(non-strict)linear matrix inequalities over a multi-agent network,where each agent only knows one inequality,and all agents co-operate to reach a cons...In this paper,we develop a distributed solver for a group of strict(non-strict)linear matrix inequalities over a multi-agent network,where each agent only knows one inequality,and all agents co-operate to reach a consensus solution in the intersection of all the feasible regions.The formulation is transformed into a distributed optimization problem by introducing slack variables and consensus constraints.Then,by the primal–dual methods,a distributed algorithm is proposed with the help of projection operators and derivative feedback.Finally,the convergence of the algorithm is analyzed,followed by illustrative simulations.展开更多
This paper investigates two distributed accelerated primal-dual neurodynamic approaches over undirected connected graphs for resource allocation problems(RAP)where the objective functions are generally convex.With the...This paper investigates two distributed accelerated primal-dual neurodynamic approaches over undirected connected graphs for resource allocation problems(RAP)where the objective functions are generally convex.With the help of projection operators,a primal-dual framework,and Nesterov's accelerated method,we first design a distributed accelerated primal-dual projection neurodynamic approach(DAPDP),and its convergence rate of the primal-dual gap is O(1/(t^(2)))by selecting appropriate parameters and initial values.Then,when the local closed convex sets are convex inequalities which have no closed-form solutions of their projection operators,we further propose a distributed accelerated penalty primal-dual neurodynamic approach(DAPPD)on the strength of the penalty method,primal-dual framework,and Nesterov's accelerated method.Based on the above analysis,we prove that DAPPD also has a convergence rate O(1/(t^(2)))of the primal-dual gap.Compared with the distributed dynamical approaches based on the classical primal-dual framework,our proposed distributed accelerated neurodynamic approaches have faster convergence rates.Numerical simulations demonstrate that our proposed neurodynamic approaches are feasible and effective.展开更多
In this paper,we introduce for the first time a new eligible kernel function with a hyperbolic barrier term for semidefinite programming(SDP).This add a new type of functions to the class of eligible kernel functions....In this paper,we introduce for the first time a new eligible kernel function with a hyperbolic barrier term for semidefinite programming(SDP).This add a new type of functions to the class of eligible kernel functions.We prove that the interior-point algorithm based on the new kernel function meets O(n3/4 logε/n)iterations as the worst case complexity bound for the large-update method.This coincides with the complexity bound obtained by the first kernel function with a trigonometric barrier term proposed by El Ghami et al.in2012,and improves with a factor n(1/4)the obtained iteration bound based on the classic kernel function.We present some numerical simulations which show the effectiveness of the algorithm developed in this paper.展开更多
Image segmentation is a hot topic in image science. In this paper we present a new variational segmentation model based on the theory of Mumford-Shah model. The aim of our model is to divide noised image, according to...Image segmentation is a hot topic in image science. In this paper we present a new variational segmentation model based on the theory of Mumford-Shah model. The aim of our model is to divide noised image, according to a certain criterion, into homogeneous and smooth regions that should correspond to structural units in the scene or objects of interest. The proposed region-based model uses total variation as a regularization term, and different fidelity term can be used for image segmentation in the cases of physical noise, such as Gaussian, Poisson and multiplicative speckle noise. Our model consists of five weighted terms, two of them are responsible for image denoising based on fidelity term and total variation term, the others assure that the three conditions of adherence to the data, smoothing, and discontinuity detection are met at once. We also develop a primal-dual hybrid gradient algorithm for our model. Numerical results on various synthetic and real images are provided to compare our method with others, these results show that our proposed model and algorithms are effective.展开更多
This paper presents a TOPF （three-phase optimal power flow） model that represents photovoltaic systems. The PV plant is modeled in the TOPF as active and reactive power source. Reactive power can be generated or abs...This paper presents a TOPF （three-phase optimal power flow） model that represents photovoltaic systems. The PV plant is modeled in the TOPF as active and reactive power source. Reactive power can be generated or absorbed using the available capacity and the adjustable power factor of the inverter. The reduction of unbalance voltage and losses in the distribution systems is obtained by actions of reactive power control of the inverter. The TOPF is formulated by current balance equations and the PV systems are modeled via an equivalent circuit. The primal-dual interior point method is used to obtain the optimal operating points for the systems for different scenarios of solar irradiance and temperature, thus providing a detailed view of the impact of photovoltaic distributed generation.展开更多
基金National Natural Science Foundations of China(Nos.61301229,61101208)Doctoral Research Funds of Henan University of Science and Technology,China(Nos.09001708,09001751)
文摘To preserve the edges and details of the image,a new variational model for wavelet domain inpainting was proposed which contained a non-convex regularizer. The non-convex regularizer can utilize the local information of image and perform better than those usual convex ones. In addition, to solve the non-convex minimization problem,an iterative reweighted method and a primaldual method were designed. The numerical experiments show that the new model not only gets better visual effects but also obtains higher signal to noise ratio than the recent method.
文摘In the present paper we present a class of polynomial primal-dual interior-point algorithms for semidefmite optimization based on a kernel function. This kernel function is not a so-called self-regular function due to its growth term increasing linearly. Some new analysis tools were developed which can be used to deal with complexity ＂analysis of the algorithms which use analogous strategy in [5] to design the search directions for the Newton system. The complexity bounds for the algorithms with large- and small-update methodswere obtained, namely,O（qn^（p＋q/q（P＋1）log n/ε and O（q^2√n）log n/ε,respectlvely.
基金Supported by the National Natural Science Foundation of China(71071119)
文摘This paper proposes an infeasible interior-point algorithm for linear complementarity problem with full-Newton steps.The main iteration consists of a feasibility step and several centrality steps.No more than O（n log（n /ε））iterations are required for getting ε-solution of the problem at hand,which coincides with the best-known bound for infeasible interior-point algorithms.
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.
基金supported in part by China NSF grant No.12001086.
文摘We present a primal-dual discontinuous Galerkin finite element method for a type of ill-posed elliptic Cauchy problem.It is shown that the discrete problem attains a unique solution,if the solution of the ill-posed elliptic Cauchy problems is unique.An optimal error estimate is obtained in a H1-like norm.Numerical experiments are provided to demonstrate the efficiency of the proposed method.
基金Supported by National Natural Science Foundation of China (Grant Nos.10771133 and 70871082)Shanghai Leading Academic Discipline Project (Grant No.S30104)
文摘Kernel functions play an important role in defining new search directions for primal-dual interior-point algorithm for solving linear optimization problems. In this paper we present a new kernel function which yields an algorithm with the best known complexity bound for both large- and small-update methods.
基金supported by National Natural Science Foundation of China(Grant Nos.1136103011271049 and 11271049)+5 种基金the Project Sponsored by the Scientific Research Foundation for the Returned Overseas Chinese ScholarsState Education Ministry(Grant Nos.CUHK400412HKBU502814211911and 12302714)Hong Kong Research Grants Council(Grant No.Ao E/M-05/12)FRGs of Hong Kong Baptist University
文摘We consider the problem of restoring images corrupted by Poisson noise. Under the framework of maximum a posteriori estimator, the problem can be converted into a minimization problem where the objective function is composed of a Kullback-Leibler(KL)-divergence term for the Poisson noise and a total variation(TV) regularization term. Due to the logarithm function in the KL-divergence term, the non-differentiability of TV term and the positivity constraint on the images, it is not easy to design stable and efficiency algorithm for the problem. Recently, many researchers proposed to solve the problem by alternating direction method of multipliers(ADMM). Since the approach introduces some auxiliary variables and requires the solution of some linear systems, the iterative procedure can be complicated. Here we formulate the problem as two new constrained minimax problems and solve them by Chambolle-Pock's first order primal-dual approach. The convergence of our approach is guaranteed by their theory. Comparing with ADMM approaches, our approach requires about half of the auxiliary variables and is matrix-inversion free. Numerical results show that our proposed algorithms are efficient and outperform the ADMM approach.
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.
文摘In this paper,an integrated guidance and control approach is presented to improve the performance of the missile interception.The approach includes damping augmented system with attitude rate feedback to decrease the oscillation during the homing phase for missiles with low damping.In addition,physical constraints,which can affect the performance of the missile interception,such as acceleration limit,seeker’s look angle,and look angle rate constraints are considered.The integrated guidance and control problem is formulated as a convex quadratic optimization problem with equality and inequality constraints,and the solution is obtained by a primal–dual interior point method.The performance of the proposed method is verified through several numerical examples.
基金This work was supported by the Shanghai Municipal Science and Technology Major Project(No.2021SHZDZX0100)the National Natural Science Foundation of China(Nos.61733018,62073035)。
文摘In this paper,we develop a distributed solver for a group of strict(non-strict)linear matrix inequalities over a multi-agent network,where each agent only knows one inequality,and all agents co-operate to reach a consensus solution in the intersection of all the feasible regions.The formulation is transformed into a distributed optimization problem by introducing slack variables and consensus constraints.Then,by the primal–dual methods,a distributed algorithm is proposed with the help of projection operators and derivative feedback.Finally,the convergence of the algorithm is analyzed,followed by illustrative simulations.
基金supported by the National Natural Science Foundation of China (Grant No.62176218)the Fundamental Research Funds for the Central Universities (Grant No.XDJK2020TY003)。
文摘This paper investigates two distributed accelerated primal-dual neurodynamic approaches over undirected connected graphs for resource allocation problems(RAP)where the objective functions are generally convex.With the help of projection operators,a primal-dual framework,and Nesterov's accelerated method,we first design a distributed accelerated primal-dual projection neurodynamic approach(DAPDP),and its convergence rate of the primal-dual gap is O(1/(t^(2)))by selecting appropriate parameters and initial values.Then,when the local closed convex sets are convex inequalities which have no closed-form solutions of their projection operators,we further propose a distributed accelerated penalty primal-dual neurodynamic approach(DAPPD)on the strength of the penalty method,primal-dual framework,and Nesterov's accelerated method.Based on the above analysis,we prove that DAPPD also has a convergence rate O(1/(t^(2)))of the primal-dual gap.Compared with the distributed dynamical approaches based on the classical primal-dual framework,our proposed distributed accelerated neurodynamic approaches have faster convergence rates.Numerical simulations demonstrate that our proposed neurodynamic approaches are feasible and effective.
文摘In this paper,we introduce for the first time a new eligible kernel function with a hyperbolic barrier term for semidefinite programming(SDP).This add a new type of functions to the class of eligible kernel functions.We prove that the interior-point algorithm based on the new kernel function meets O(n3/4 logε/n)iterations as the worst case complexity bound for the large-update method.This coincides with the complexity bound obtained by the first kernel function with a trigonometric barrier term proposed by El Ghami et al.in2012,and improves with a factor n(1/4)the obtained iteration bound based on the classic kernel function.We present some numerical simulations which show the effectiveness of the algorithm developed in this paper.
基金Supported in part by the NNSF of China(11301129,11271323,91330105,11326033)the Zhejiang Provincial Natural Science Foundation of China(LQ13A010025,LZ13A010002)
文摘Image segmentation is a hot topic in image science. In this paper we present a new variational segmentation model based on the theory of Mumford-Shah model. The aim of our model is to divide noised image, according to a certain criterion, into homogeneous and smooth regions that should correspond to structural units in the scene or objects of interest. The proposed region-based model uses total variation as a regularization term, and different fidelity term can be used for image segmentation in the cases of physical noise, such as Gaussian, Poisson and multiplicative speckle noise. Our model consists of five weighted terms, two of them are responsible for image denoising based on fidelity term and total variation term, the others assure that the three conditions of adherence to the data, smoothing, and discontinuity detection are met at once. We also develop a primal-dual hybrid gradient algorithm for our model. Numerical results on various synthetic and real images are provided to compare our method with others, these results show that our proposed model and algorithms are effective.
文摘This paper presents a TOPF （three-phase optimal power flow） model that represents photovoltaic systems. The PV plant is modeled in the TOPF as active and reactive power source. Reactive power can be generated or absorbed using the available capacity and the adjustable power factor of the inverter. The reduction of unbalance voltage and losses in the distribution systems is obtained by actions of reactive power control of the inverter. The TOPF is formulated by current balance equations and the PV systems are modeled via an equivalent circuit. The primal-dual interior point method is used to obtain the optimal operating points for the systems for different scenarios of solar irradiance and temperature, thus providing a detailed view of the impact of photovoltaic distributed generation.
