最大値関数を含む数理計画問題の最適性条件と一般勾配を用いた計算方法

抄録

We study a mathematical programming problem whose objective and constraint functions include the extremal-value functions. This problem can be regarded as an extension of well-known “min-max problem” and/or infinitely constrained problem”, and it becomes a nondifferentiable optimization problem. In this paper, we present some optimality conditions for such problem by use of a new theorem of the alternative and Gauvin's results concerned with the extremal-value functions. Moreover, as a computational method for our problem, we propose applying the Mifflin's nondifferentiable optimization algorithm by means of the generalized gradients. A numerical example is also presented.