我们为比赛和合作问题的共存在这篇论文学习一个数学编程模型。我们介绍一个新答案概念，这个问题的 s 最佳的答案，它总是在紧缩、连续的条件下面存在。一最佳的答案能被解决一个非线性的编程问题获得，这被显示出。一些例子被给解释...我们为比赛和合作问题的共存在这篇论文学习一个数学编程模型。我们介绍一个新答案概念，这个问题的 s 最佳的答案，它总是在紧缩、连续的条件下面存在。一最佳的答案能被解决一个非线性的编程问题获得，这被显示出。一些例子被给解释怎么计算一个 s 最佳的答案。展开更多
The bilevel programming is applied to solve hierarchical intelligence control problems in such fields as industry, agriculture, transportation, military, and so on. This paper presents a quadratic objective penalty fu...The bilevel programming is applied to solve hierarchical intelligence control problems in such fields as industry, agriculture, transportation, military, and so on. This paper presents a quadratic objective penalty function with two penalty parameters for inequality constrained bilevel programming.Under some conditions, the optimal solution to the bilevel programming defined by the quadratic objective penalty function is proved to be an optimal solution to the original bilevel programming.Moreover, based on the quadratic objective penalty function, an algorithm is developed to find an optimal solution to the original bilevel programming, and its convergence proved under some conditions.Furthermore, under the assumption of convexity at lower level problems, a quadratic objective penalty function without lower level problems is defined and is proved equal to the original bilevel programming.展开更多
Some classical penalty function algorithms may not always be convergent under big penalty parameters in Matlab software,which makes them impossible to find out an optimal solution to constrained optimization problems....Some classical penalty function algorithms may not always be convergent under big penalty parameters in Matlab software,which makes them impossible to find out an optimal solution to constrained optimization problems.In this paper,a novel penalty function(called M-objective penalty function) with one penalty parameter added to both objective and constrained functions of inequality constrained optimization problems is proposed.Based on the M-objective penalty function,an algorithm is developed to solve an optimal solution to the inequality constrained optimization problems,with its convergence proved under some conditions.Furthermore,numerical results show that the proposed algorithm has a much better convergence than the classical penalty function algorithms under big penalty parameters,and is efficient in choosing a penalty parameter in a large range in Matlab software.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.11271329 and 10971193
文摘The bilevel programming is applied to solve hierarchical intelligence control problems in such fields as industry, agriculture, transportation, military, and so on. This paper presents a quadratic objective penalty function with two penalty parameters for inequality constrained bilevel programming.Under some conditions, the optimal solution to the bilevel programming defined by the quadratic objective penalty function is proved to be an optimal solution to the original bilevel programming.Moreover, based on the quadratic objective penalty function, an algorithm is developed to find an optimal solution to the original bilevel programming, and its convergence proved under some conditions.Furthermore, under the assumption of convexity at lower level problems, a quadratic objective penalty function without lower level problems is defined and is proved equal to the original bilevel programming.
基金supported by the National Natural Science Foundation of China under Grant No.11271329
文摘Some classical penalty function algorithms may not always be convergent under big penalty parameters in Matlab software,which makes them impossible to find out an optimal solution to constrained optimization problems.In this paper,a novel penalty function(called M-objective penalty function) with one penalty parameter added to both objective and constrained functions of inequality constrained optimization problems is proposed.Based on the M-objective penalty function,an algorithm is developed to solve an optimal solution to the inequality constrained optimization problems,with its convergence proved under some conditions.Furthermore,numerical results show that the proposed algorithm has a much better convergence than the classical penalty function algorithms under big penalty parameters,and is efficient in choosing a penalty parameter in a large range in Matlab software.
