多目标minimax问题的极大熵方法及其收敛性

A Maximum Entropy Method for Multiobjective Minimax Problems and Its Convergence

研究了多目标ｍｉｎｉｍａｘ问题的极大熵方法的构成．

By using the idea that a complicated problem can be approximated by a simple and easily solved one so that a complicated nondifferentiable problem can be solved by solving a simpler differentiable one, the structure of a maximum entropy method for solving a class of multiobjective minimax problems is studied. In order to guarantee the reliability of the solution, the properties of the gradient limit of the approximating function are investigated. It is proved that any limit point of the Fritz John point range of an approximating problem is the Fritz John point of the original multiobjective minimax problem under weaker conditions. Furthermore, by employing the concept of generalized linear independence, the relation between the Kuhn Tucker points of the approximating problem and the original one is obtained.