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
All the possible CP-conserving non-linear operators up to the p^4-order in the Lagrangian expansion are analysed here for the left-right symmetric model in the non-linear electroweak chiral context coupled to a light ...All the possible CP-conserving non-linear operators up to the p^4-order in the Lagrangian expansion are analysed here for the left-right symmetric model in the non-linear electroweak chiral context coupled to a light dynamical Higgs. The low energy effects will be triggered by an emerging new physics field content in the nature, more specifically,from spin-1 resonances sourced by the straightforward extension of the SM local gauge symmetry to the larger local group SU(2)_L × SU(2)_R× U(1)_(B-L). Low energy phenomenology will be altered by integrating out the resonances from the physical spectrum, being manifested through induced corrections onto the left handed operators. Such modifications are weighted by powers of the scales ratio implied by the symmetries of the model and will determine the size of the effective operator basis to be used. The recently observed diboson excess around the invariant mass 1.8 TeV–2 TeV entails a scale suppression that suggests to encode the low energy effects via a much smaller set of effective operators.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.
基金KITPC financial support during the completion of this work
文摘All the possible CP-conserving non-linear operators up to the p^4-order in the Lagrangian expansion are analysed here for the left-right symmetric model in the non-linear electroweak chiral context coupled to a light dynamical Higgs. The low energy effects will be triggered by an emerging new physics field content in the nature, more specifically,from spin-1 resonances sourced by the straightforward extension of the SM local gauge symmetry to the larger local group SU(2)_L × SU(2)_R× U(1)_(B-L). Low energy phenomenology will be altered by integrating out the resonances from the physical spectrum, being manifested through induced corrections onto the left handed operators. Such modifications are weighted by powers of the scales ratio implied by the symmetries of the model and will determine the size of the effective operator basis to be used. The recently observed diboson excess around the invariant mass 1.8 TeV–2 TeV entails a scale suppression that suggests to encode the low energy effects via a much smaller set of effective operators.
