uv-decomposition method for solving a mathematical program with equilibrium constraints （MPEC） problem with linear complementarity constraints is presented. The problem is first converted into a nonlinear programmin...uv-decomposition method for solving a mathematical program with equilibrium constraints （MPEC） problem with linear complementarity constraints is presented. The problem is first converted into a nonlinear programming one. The structure of subdifferential a corresponding penalty function and results of its uv-decomposition are given. A conceptual algorithm for solving this problem with a superUnear convergence rate is then constructed in terms of the obtained results.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
基金Project supported by the National Natural Science Foundation of China(Nos.10372063,10771026 and 10471015)
文摘uv-decomposition method for solving a mathematical program with equilibrium constraints （MPEC） problem with linear complementarity constraints is presented. The problem is first converted into a nonlinear programming one. The structure of subdifferential a corresponding penalty function and results of its uv-decomposition are given. A conceptual algorithm for solving this problem with a superUnear convergence rate is then constructed in terms of the obtained results.
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.
