We consider the problems of minimizing the sum of a continuously differentiable convex function and a nonsmooth convex function in this paper. These problems arise in many applications of practical interest.A class of...We consider the problems of minimizing the sum of a continuously differentiable convex function and a nonsmooth convex function in this paper. These problems arise in many applications of practical interest.A class of alternating linearization methods is presented for solving these problems. The global convergence rate is also obtained under certain mild conditions. Numerical experiments validate the theoretical convergence analysis and verify the implementation of the proposed algorithm.展开更多
In this paper we study optimization problems involving convex nonlinear semidefinite programming(CSDP).Here we convert CSDP into eigenvalue problem by exact penalty function,and apply the U-Lagrangian theory to the fu...In this paper we study optimization problems involving convex nonlinear semidefinite programming(CSDP).Here we convert CSDP into eigenvalue problem by exact penalty function,and apply the U-Lagrangian theory to the function of the largest eigenvalues,with matrix-convex valued mappings.We give the first-and second-order derivatives of U-Lagrangian in the space of decision variables Rm when transversality condition holds.Moreover,an algorithm frame with superlinear convergence is presented.Finally,we give one application:bilinear matrix inequality(BMI)optimization;meanwhile,list their UV decomposition results.展开更多
The form of a dual problem of Mond-Weir type for multi-objective programming problems of generalized functions is defined and theorems of the weak duality, direct duality and inverse duality are proven.
In this paper, the uV-theory and P-differential calculus are employed to study second-order expansion of a class of D,C, functions and minimization problems. Under certain conditions, some properties of the u-Lagrangi...In this paper, the uV-theory and P-differential calculus are employed to study second-order expansion of a class of D,C, functions and minimization problems. Under certain conditions, some properties of the u-Lagrangian, the second-order expansion of this class of functions along some trajectories are formulated. Some first and second order optimality conditions for the class of D,C, optimization problems are given.展开更多
基金partially supported by the National Natural Science Foundation of China(No.11501074,11701061,61877032)the Funds of Doctoral Start-Up of Liaoning Province(No.201501194)+1 种基金the Funds of National Science of Liaoning Province(No.20170540652)Huzhou Science and Technology Plan(No.2016GY03)
文摘We consider the problems of minimizing the sum of a continuously differentiable convex function and a nonsmooth convex function in this paper. These problems arise in many applications of practical interest.A class of alternating linearization methods is presented for solving these problems. The global convergence rate is also obtained under certain mild conditions. Numerical experiments validate the theoretical convergence analysis and verify the implementation of the proposed algorithm.
基金This paper is supported by the National Natural Science Foundation of China(Nos.11701063,11901075)the Project funded by China Postdoctoral Science Foundation(Nos.2019M651091,2019M661073)+5 种基金the Fundamental Research Funds for the Central Universities(Nos.3132021193,3132021199)the Natural Science Foundation of Liaoning Province in China(Doctoral Startup Foundation of Liaoning Province in China(Nos.2020-BS-074)Dalian Youth Science and Technology Star(No.2020RQ047)Huzhou Science and Technology Plan(No.2016GY03)Key Research and Development Projects of Shandong Province(No.2019GGX104089)the Natural Science Foundation of Shandong Province(No.ZR2019BA014).
文摘In this paper we study optimization problems involving convex nonlinear semidefinite programming(CSDP).Here we convert CSDP into eigenvalue problem by exact penalty function,and apply the U-Lagrangian theory to the function of the largest eigenvalues,with matrix-convex valued mappings.We give the first-and second-order derivatives of U-Lagrangian in the space of decision variables Rm when transversality condition holds.Moreover,an algorithm frame with superlinear convergence is presented.Finally,we give one application:bilinear matrix inequality(BMI)optimization;meanwhile,list their UV decomposition results.
基金Supported by the State Foundation of Ph.D.Units(No.20020141013)the National Natural Science Foundation of China(No.10471015)the Tianyuan Foundation of Natural Science Foundation of China(No.10426008)
文摘The form of a dual problem of Mond-Weir type for multi-objective programming problems of generalized functions is defined and theorems of the weak duality, direct duality and inverse duality are proven.
基金Supported by the Foundations of Ph.D.Units,the Ministry of Education(20020141013)National Natural Science Foundation of China(No.10001007)
文摘In this paper, the uV-theory and P-differential calculus are employed to study second-order expansion of a class of D,C, functions and minimization problems. Under certain conditions, some properties of the u-Lagrangian, the second-order expansion of this class of functions along some trajectories are formulated. Some first and second order optimality conditions for the class of D,C, optimization problems are given.
