Dear Editor,This letter proposes a convex optimization-based model predictive control(MPC)autonomous guidance method for the Mars ascent vehicle(MAV).We use the modified chebyshev-picard iteration(MCPI)to solve optimi...Dear Editor,This letter proposes a convex optimization-based model predictive control(MPC)autonomous guidance method for the Mars ascent vehicle(MAV).We use the modified chebyshev-picard iteration(MCPI)to solve optimization sub-problems within the MPC framework,eliminating the dynamic constraints in solving the optimal control problem and enhancing the convergence performance of the algorithm.Moreover,this method can repeatedly perform trajectory optimization calculations at a high frequency,achieving timely correction of the optimal control command.Numerical simulations demonstrate that the method can satisfy the requirements of rapid computation and reliability for the MAV system when considering uncertainties and perturbations.展开更多
The authors of this article are interested in characterization of efficient solutions for special classes of problems. These classes consider semi-strong E-convexity of involved functions. Sufficient and necessary con...The authors of this article are interested in characterization of efficient solutions for special classes of problems. These classes consider semi-strong E-convexity of involved functions. Sufficient and necessary conditions for a feasible solution to be an efficient or properly efficient solution are obtained.展开更多
The optimization problem is considered in which the objective function is pseudolinear（both pseudoconvex and pseudoconcave） and the constraints are linear. The general expression for the optimal solutions to the pro...The optimization problem is considered in which the objective function is pseudolinear（both pseudoconvex and pseudoconcave） and the constraints are linear. The general expression for the optimal solutions to the problem is derived with the representation theorem of polyhedral sets, and the uniqueness condition of the optimal solution and the computational procedures to determine all optimal solutions （if the uniqueness condition is not satisfied ） are provided. Finally, an illustrative example is also given.展开更多
This paper primarily focuses on solving the Heilbronn problem of convex polygons,which involves minimizing the area of a convex polygon P_(1)P_(2)···P_(n) while satisfying the condition that the areas o...This paper primarily focuses on solving the Heilbronn problem of convex polygons,which involves minimizing the area of a convex polygon P_(1)P_(2)···P_(n) while satisfying the condition that the areas of all triangles formed by consecutive vertices are equal to 1/2.The problem is reformulated as a polynomial optimization problem with a bilinear objective function and bilinear constraints.A new method is presented to verify the upper and lower bounds for the optimization problem.The upper bound is obtained by the affine regular decagon.Then Bilinear Matrix Inequalities(BMI)theory and the branch-and-bound technique are used to verify the lower bound of the problem.The paper concludes by proving that the lower bound for the area minimization problem of a convex polygon with 10 vertices is 13.076548.The relative error compared to the global optimum is 0.104%.展开更多
In this paper,we consider a more general bi-level optimization problem,where the inner objective function is consisted of three convex functions,involving a smooth and two non-smooth functions.The outer objective func...In this paper,we consider a more general bi-level optimization problem,where the inner objective function is consisted of three convex functions,involving a smooth and two non-smooth functions.The outer objective function is a classical strongly convex function which may not be smooth.Motivated by the smoothing approaches,we modify the classical bi-level gradient sequential averaging method to solve the bi-level optimization problem.Under some mild conditions,we obtain the convergence rate of the generated sequence,and then based on the analysis framework of S-FISTA,we show the global convergence rate of the proposed algorithm.展开更多
In this paper, we consider the composed convex optimization problem which consists in minimizing the sum of a convex function and a convex composite function. By using the properties of the epigraph of the conjugate f...In this paper, we consider the composed convex optimization problem which consists in minimizing the sum of a convex function and a convex composite function. By using the properties of the epigraph of the conjugate functions and the subdifferentials of convex functions, we give some new constraint qualifications which completely characterize the strong Fenchel duality and the total Fenchel duality for composed convex optimiztion problem in real locally convex Hausdorff topological vector spaces.展开更多
In this paper, the nonlinear programming problem with quasimonotonic （ both quasiconvex and quasiconcave ）objective function and linear constraints is considered. With the decomposition theorem of polyhedral sets, t...In this paper, the nonlinear programming problem with quasimonotonic （ both quasiconvex and quasiconcave ）objective function and linear constraints is considered. With the decomposition theorem of polyhedral sets, the structure of optimal solution set for the programming problem is depicted. Based on a simplified version of the convex simplex method, the uniqueness condition of optimal solution and the computational procedures to determine all optimal solutions are given, if the uniqueness condition is not satisfied. An illustrative example is also presented.展开更多
The purpose of this paper is to study the approximate optimality condition for composite convex optimization problems with a cone-convex system in locally convex spaces,where all functions involved are not necessaril...The purpose of this paper is to study the approximate optimality condition for composite convex optimization problems with a cone-convex system in locally convex spaces,where all functions involved are not necessarily lower semicontinuous.By using the properties of the epigraph of conjugate functions,we introduce a new regularity condition and give its equivalent characterizations.Under this new regularity condition,we derive necessary and sufficient optimality conditions ofε-optimal solutions for the composite convex optimization problem.As applications of our results,we derive approximate optimality conditions to cone-convex optimization problems.Our results extend or cover many known results in the literature.展开更多
In this paper, firstly, we propose several convexification and concavification transformations to convert a strictly monotone function into a convex or concave function, then we propose several convexification and con...In this paper, firstly, we propose several convexification and concavification transformations to convert a strictly monotone function into a convex or concave function, then we propose several convexification and concavification transformations to convert a non-convex and non-concave objective function into a convex or concave function in the programming problems with convex or concave constraint functions, and propose several convexification and concavification transformations to convert a non-monotone objective function into a convex or concave function in some programming problems with strictly monotone constraint functions. Finally, we prove that the original programming problem can be converted into an equivalent concave minimization problem, or reverse convex programming problem or canonical D.C. programming problem. Then the global optimal solution of the original problem can be obtained by solving the converted concave minimization problem, or reverse convex programming problem or canonical D.C. programming problem using the existing algorithms about them.展开更多
For a multiobjective bilevel programnfing problem （P） with an extremal-value function, its dual problem is constructed by using the Fenchel-Moreau conjugate of the functions involved. Under some convexity and monoto...For a multiobjective bilevel programnfing problem （P） with an extremal-value function, its dual problem is constructed by using the Fenchel-Moreau conjugate of the functions involved. Under some convexity and monotonicity assumptions, the weak and strong duality assertions are obtained.展开更多
Accelerated proximal gradient methods have recently been developed for solving quasi-static incremental problems of elastoplastic analysis with some different yield criteria.It has been demonstrated through numerical ...Accelerated proximal gradient methods have recently been developed for solving quasi-static incremental problems of elastoplastic analysis with some different yield criteria.It has been demonstrated through numerical experiments that these methods can outperform conventional optimization-based approaches in computational plasticity.However,in literature these algorithms are described individually for specific yield criteria,and hence there exists no guide for application of the algorithms to other yield criteria.This short paper presents a general form of algorithm design,independent of specific forms of yield criteria,that unifies the existing proximal gradient methods.Clear interpretation is also given to each step of the presented general algorithm so that each update rule is linked to the underlying physical laws in terms of mechanical quantities.展开更多
In this paper we introduce a method to construct periodic solutions for the n-body problem with only boundary and topological constraints.Our approach is based on some novel features of the Keplerian action functional...In this paper we introduce a method to construct periodic solutions for the n-body problem with only boundary and topological constraints.Our approach is based on some novel features of the Keplerian action functional,constraint convex optimization techniques,and variational methods.We demonstrate the strength of this method by constructing relative periodic solutions for the planar four-body problem within a special topological class,and our results hold for an open set of masses.展开更多
This paper proposes a new level-set-based shape recovery approach that can be applied to a wide range of binary tomography reconstructions.In this technique,we derive generic evolution equations for shape reconstructi...This paper proposes a new level-set-based shape recovery approach that can be applied to a wide range of binary tomography reconstructions.In this technique,we derive generic evolution equations for shape reconstruction in terms of the underlying level-set parameters.We show that using the appropriate basis function to parameterize the level-set function results in an optimization problem with a small number of parameters,which overcomes many of the problems associated with the traditional level-set approach.More concretely,in this paper,we use Gaussian functions as a basis function placed at sparse grid points to represent the parametric level-set function and provide more flexibility in the binary representation of the reconstructed image.In addition,we suggest a convex optimization method that can overcome the problem of the local minimum of the cost function by successfully recovering the coefficients of the basis function.Finally,we illustrate the performance of the proposed method using synthetic images and real X-ray CT projection data.We show that the proposed reconstruction method compares favorably to various state-of-the-art reconstruction techniques for limited-data tomography,and it is also relatively stable in the presence of modest amounts of noise.Furthermore,the shape representation using a compact Gaussian radial basis function works well.展开更多
A control problem containing support functions in the integrand of the objective of the functional as well as in the inequality constraint function is considered. For this problem, Fritz John and Karush-Kuhn-Tucker ty...A control problem containing support functions in the integrand of the objective of the functional as well as in the inequality constraint function is considered. For this problem, Fritz John and Karush-Kuhn-Tucker type necessary optimality conditions are derived. Using Karush-Kuhn-Tucker type optimality conditions, Wolfe type dual is formulated and usual duality theorems are established under generalized convexity conditions. Special cases are generated. It is also shown that our duality results have linkage with those of nonlinear programming problems involving support functions.展开更多
Superconvergence and recovery a posteriori error estimates of the finite element ap- proximation for general convex optimal control problems are investigated in this paper. We obtain the superconvergence properties of...Superconvergence and recovery a posteriori error estimates of the finite element ap- proximation for general convex optimal control problems are investigated in this paper. We obtain the superconvergence properties of finite element solutions, and by using the superconvergence results we get recovery a posteriori error estimates which are asymptotically exact under some regularity conditions. Some numerical examples are provided to verify the theoretical results.展开更多
基金supported by the National Defense Basic Scientific Research Program(JCKY2021603B030)the National Natural Science Foundation of China(62273118,12150008)the Natural Science Foundation of Heilongjiang Province(LH2022F023).
文摘Dear Editor,This letter proposes a convex optimization-based model predictive control(MPC)autonomous guidance method for the Mars ascent vehicle(MAV).We use the modified chebyshev-picard iteration(MCPI)to solve optimization sub-problems within the MPC framework,eliminating the dynamic constraints in solving the optimal control problem and enhancing the convergence performance of the algorithm.Moreover,this method can repeatedly perform trajectory optimization calculations at a high frequency,achieving timely correction of the optimal control command.Numerical simulations demonstrate that the method can satisfy the requirements of rapid computation and reliability for the MAV system when considering uncertainties and perturbations.
文摘The authors of this article are interested in characterization of efficient solutions for special classes of problems. These classes consider semi-strong E-convexity of involved functions. Sufficient and necessary conditions for a feasible solution to be an efficient or properly efficient solution are obtained.
文摘The optimization problem is considered in which the objective function is pseudolinear（both pseudoconvex and pseudoconcave） and the constraints are linear. The general expression for the optimal solutions to the problem is derived with the representation theorem of polyhedral sets, and the uniqueness condition of the optimal solution and the computational procedures to determine all optimal solutions （if the uniqueness condition is not satisfied ） are provided. Finally, an illustrative example is also given.
基金supported by the National Natural Science Foundation of China under Grant No.12171159the National Natural Science Fund of China Research Fund for International Scientists under Grant No.12350410363。
文摘This paper primarily focuses on solving the Heilbronn problem of convex polygons,which involves minimizing the area of a convex polygon P_(1)P_(2)···P_(n) while satisfying the condition that the areas of all triangles formed by consecutive vertices are equal to 1/2.The problem is reformulated as a polynomial optimization problem with a bilinear objective function and bilinear constraints.A new method is presented to verify the upper and lower bounds for the optimization problem.The upper bound is obtained by the affine regular decagon.Then Bilinear Matrix Inequalities(BMI)theory and the branch-and-bound technique are used to verify the lower bound of the problem.The paper concludes by proving that the lower bound for the area minimization problem of a convex polygon with 10 vertices is 13.076548.The relative error compared to the global optimum is 0.104%.
文摘In this paper,we consider a more general bi-level optimization problem,where the inner objective function is consisted of three convex functions,involving a smooth and two non-smooth functions.The outer objective function is a classical strongly convex function which may not be smooth.Motivated by the smoothing approaches,we modify the classical bi-level gradient sequential averaging method to solve the bi-level optimization problem.Under some mild conditions,we obtain the convergence rate of the generated sequence,and then based on the analysis framework of S-FISTA,we show the global convergence rate of the proposed algorithm.
基金Supported by the National Natural Science Foundation of China(No.11461027)Hunan Provincial Natural Science Foundation of China(No.2016JJ2099)the Scientific Research Fund of Hunan Provincial Education Department(No.17A172)
文摘In this paper, we consider the composed convex optimization problem which consists in minimizing the sum of a convex function and a convex composite function. By using the properties of the epigraph of the conjugate functions and the subdifferentials of convex functions, we give some new constraint qualifications which completely characterize the strong Fenchel duality and the total Fenchel duality for composed convex optimiztion problem in real locally convex Hausdorff topological vector spaces.
基金Supported by the Research Foundation of Jinan University(04SKZD01).
文摘In this paper, the nonlinear programming problem with quasimonotonic （ both quasiconvex and quasiconcave ）objective function and linear constraints is considered. With the decomposition theorem of polyhedral sets, the structure of optimal solution set for the programming problem is depicted. Based on a simplified version of the convex simplex method, the uniqueness condition of optimal solution and the computational procedures to determine all optimal solutions are given, if the uniqueness condition is not satisfied. An illustrative example is also presented.
基金the National Natural Science Foundation of China(Nos.11471059,11301571,and 11301570)the Chongqing Research Program of Basic Research and Frontier Technology(Nos.cstc2014jcyjA00037,cstc2015jcyjB00001,cstc2015jcyjA00025,and cstc2015jcyjA00002)+2 种基金the Education Committee Project Research Foundation of Chongqing(Nos.KJ1400618 and KJ1500626)the Postdoctoral Science Foundation of China(Nos.2015M580774 and 2016T90837)the Program for University Innovation Team of Chongqing(CXTDX201601026 and CXTDX201601022).
文摘The purpose of this paper is to study the approximate optimality condition for composite convex optimization problems with a cone-convex system in locally convex spaces,where all functions involved are not necessarily lower semicontinuous.By using the properties of the epigraph of conjugate functions,we introduce a new regularity condition and give its equivalent characterizations.Under this new regularity condition,we derive necessary and sufficient optimality conditions ofε-optimal solutions for the composite convex optimization problem.As applications of our results,we derive approximate optimality conditions to cone-convex optimization problems.Our results extend or cover many known results in the literature.
基金This research is supported by the National Natural Science Foundation of China(Grant 10271073).
文摘In this paper, firstly, we propose several convexification and concavification transformations to convert a strictly monotone function into a convex or concave function, then we propose several convexification and concavification transformations to convert a non-convex and non-concave objective function into a convex or concave function in the programming problems with convex or concave constraint functions, and propose several convexification and concavification transformations to convert a non-monotone objective function into a convex or concave function in some programming problems with strictly monotone constraint functions. Finally, we prove that the original programming problem can be converted into an equivalent concave minimization problem, or reverse convex programming problem or canonical D.C. programming problem. Then the global optimal solution of the original problem can be obtained by solving the converted concave minimization problem, or reverse convex programming problem or canonical D.C. programming problem using the existing algorithms about them.
基金Supported by the National Natural Science Foundation of China(Grant No.11171250)
文摘For a multiobjective bilevel programnfing problem （P） with an extremal-value function, its dual problem is constructed by using the Fenchel-Moreau conjugate of the functions involved. Under some convexity and monotonicity assumptions, the weak and strong duality assertions are obtained.
文摘Accelerated proximal gradient methods have recently been developed for solving quasi-static incremental problems of elastoplastic analysis with some different yield criteria.It has been demonstrated through numerical experiments that these methods can outperform conventional optimization-based approaches in computational plasticity.However,in literature these algorithms are described individually for specific yield criteria,and hence there exists no guide for application of the algorithms to other yield criteria.This short paper presents a general form of algorithm design,independent of specific forms of yield criteria,that unifies the existing proximal gradient methods.Clear interpretation is also given to each step of the presented general algorithm so that each update rule is linked to the underlying physical laws in terms of mechanical quantities.
文摘In this paper we introduce a method to construct periodic solutions for the n-body problem with only boundary and topological constraints.Our approach is based on some novel features of the Keplerian action functional,constraint convex optimization techniques,and variational methods.We demonstrate the strength of this method by constructing relative periodic solutions for the planar four-body problem within a special topological class,and our results hold for an open set of masses.
基金This work was supported by JST-CREST Grant Number JPMJCR1765,Japan.
文摘This paper proposes a new level-set-based shape recovery approach that can be applied to a wide range of binary tomography reconstructions.In this technique,we derive generic evolution equations for shape reconstruction in terms of the underlying level-set parameters.We show that using the appropriate basis function to parameterize the level-set function results in an optimization problem with a small number of parameters,which overcomes many of the problems associated with the traditional level-set approach.More concretely,in this paper,we use Gaussian functions as a basis function placed at sparse grid points to represent the parametric level-set function and provide more flexibility in the binary representation of the reconstructed image.In addition,we suggest a convex optimization method that can overcome the problem of the local minimum of the cost function by successfully recovering the coefficients of the basis function.Finally,we illustrate the performance of the proposed method using synthetic images and real X-ray CT projection data.We show that the proposed reconstruction method compares favorably to various state-of-the-art reconstruction techniques for limited-data tomography,and it is also relatively stable in the presence of modest amounts of noise.Furthermore,the shape representation using a compact Gaussian radial basis function works well.
文摘A control problem containing support functions in the integrand of the objective of the functional as well as in the inequality constraint function is considered. For this problem, Fritz John and Karush-Kuhn-Tucker type necessary optimality conditions are derived. Using Karush-Kuhn-Tucker type optimality conditions, Wolfe type dual is formulated and usual duality theorems are established under generalized convexity conditions. Special cases are generated. It is also shown that our duality results have linkage with those of nonlinear programming problems involving support functions.
基金supported by Guangdong Provincial"Zhujiang Scholar Award Project"National Science Foundation of China 10671163+2 种基金the National Basic Research Program under the Grant 2005CB321703Scientific Research Fund of Hunan Provincial Education Department 06A069Guangxi Natural Science Foundation 0575029
文摘Superconvergence and recovery a posteriori error estimates of the finite element ap- proximation for general convex optimal control problems are investigated in this paper. We obtain the superconvergence properties of finite element solutions, and by using the superconvergence results we get recovery a posteriori error estimates which are asymptotically exact under some regularity conditions. Some numerical examples are provided to verify the theoretical results.
