CAJ | 학술논문

本文讨论了一类指标集依赖于决策变量的广义半无限规划(GSMMP).首先通过刻画目标函数的Clarke导数和Clarke次微分,建立其一阶最优性条件.其次,通过对下层问题Q(x)进行扰动分析,我们得到Q(x)的一个精确罚表示.由此,利用一组精确罚函数将(GSMMP)转化为经典的半无限极大极小规划,从而可利用已有的经典半无限规划的算法来对(GSMMP)进行求解.
본문토론료일류지표집의뢰우결책변량적엄의반무한규화(GSMMP).수선통과각화목표함수적Clarke도수화Clarke차미분,건립기일계최우성조건.기차,통과대하층문제Q(x)진행우동분석,아문득도Q(x)적일개정학벌표시.유차,이용일조정학벌함수장(GSMMP)전화위경전적반무한겁대겁소규화,종이가이용이유적경전반무한규화적산법래대(GSMMP)진행구해.
This paper deals with a class of generalized semi-infinite min-max pro-gramming (GSMMP), in which the index set depends on the decision variable. Based on some new characterizations of the Clarke derivative and Clarke subdifferential of the ob-jective function, we develop the first-order optimality conditions for (GSMMP) in terms of second-order multipliers. Moreover, by addressing the perturbed problem of the lower-level programming Q(x), we obtain an exact penalty representations for Q(x), which allows us to convert (GSMMP) into the standard semi-infinite rain-max programming via a class of exact penalty functions. This fact makes it possible to solve (GSMMP) by using any available standard semi-infinite optimization algorithms.