针对只含有不等式约束的优化问题,本文首先给出了其Karush-Kuhn-Tucker (KKT)条件,并利用光滑互补函数将KKT系统转化为一类光滑的方程组问题;其次,将光滑方程组问题转化为无约束优化问题;最后,本文提出一类二阶微分方程系统求解无约束...针对只含有不等式约束的优化问题,本文首先给出了其Karush-Kuhn-Tucker (KKT)条件,并利用光滑互补函数将KKT系统转化为一类光滑的方程组问题;其次,将光滑方程组问题转化为无约束优化问题;最后,本文提出一类二阶微分方程系统求解无约束优化问题,并讨论了二阶微分方程系统的解的稳定性及收敛速度。For optimization problems with only inequality constraints, this paper first presents their Karush-Kuhn-Tucker (KKT) conditions, and uses smooth complementarity functions to transform the KKT system into a class of smooth system of equations problems. Secondly, this article transforms the problem of smooth equation systems into an unconstrained optimization problem. Finally, this article proposes a class of second-order differential equation systems for solving unconstrained optimization problems, and discusses the stability and convergence speed of the solutions of second-order differential equation systems.展开更多
基金Supported by the National Natural Science Foundation (10961006)Guangxi Education Department Science Foundation (200911LX53)Guangxi Normal University Research Foundation for the Youth Backbone Teacher of China
文摘针对只含有不等式约束的优化问题,本文首先给出了其Karush-Kuhn-Tucker (KKT)条件,并利用光滑互补函数将KKT系统转化为一类光滑的方程组问题;其次,将光滑方程组问题转化为无约束优化问题;最后,本文提出一类二阶微分方程系统求解无约束优化问题,并讨论了二阶微分方程系统的解的稳定性及收敛速度。For optimization problems with only inequality constraints, this paper first presents their Karush-Kuhn-Tucker (KKT) conditions, and uses smooth complementarity functions to transform the KKT system into a class of smooth system of equations problems. Secondly, this article transforms the problem of smooth equation systems into an unconstrained optimization problem. Finally, this article proposes a class of second-order differential equation systems for solving unconstrained optimization problems, and discusses the stability and convergence speed of the solutions of second-order differential equation systems.
