merit function

Firstly,the mixed-integer bi-level programming is transformed into a single level continuous optimization problem by virtue of penalty function concept and optimal value function tool.

利用罚函数思想和最优值函数的概念将混合整数双层规划转化为连续变量的单层非线性规划,然后用事先确定步长的凸组合算法迭代求解此单层非线性规划,进而得到原双层规划的局部最优解。

In the paper,We define a kind of continuous concepts of optimal value function on point-to-set maps and discuss the continuity of optimal value function on point-to-set maps.

给出了集值映射的连续性概念,讨论了集值映射上最优值函数的连续性,给出在不等式约束、等式和不等式约束情况下最优值函数的连续性定理,并针对最优值函数的方向导数给出了一个在新的约束规格条件下,最优值函数的连续性定理。

A set of first-order necessary optimality conditions based on the the upper and lower bounds of directional derivatives of the optimal value function of lower problem are proposed.

首先,利用下层问题最优值函数的方向导数的上下界的性质给出一阶最优性条件。