CAJ | 학술논문

垂直互补约束数学规划问题在工程设计、生产计划、优化控制等方面有很多应用。本文提出了一种求解垂直互补约束数学规划问题的松弛方法，并证明了：在垂直互补约束数学规划问题线性独立的约束规范条件下，松弛问题稳定点的任何聚点是原问题的C-稳定点。如果进一步还满足二阶必要性条件，则这些聚点是M-稳定点。基本数值结果表明提出的方法可以很好的求解垂直互补约束数学规划问题。
수직호보약속수학규화문제재공정설계、생산계화、우화공제등방면유흔다응용。본문제출료일충구해수직호보약속수학규화문제적송이방법，병증명료：재수직호보약속수학규화문제선성독립적약속규범조건하，송이문제은정점적임하취점시원문제적C-은정점。여과진일보환만족이계필요성조건，칙저사취점시M-은정점。기본수치결과표명제출적방법가이흔호적구해수직호보약속수학규화문제。
Mathematical program with vertical complementarity constraints (MPVCC) has many applications in various fields such as engineering design, manufacturing plan, optimal control and mathematical programming itself. We present a relaxation method for MPVCC. We show that, under the MPVCC linear independence con-straint qualification, any limiting point of stationary points of the relaxed problems is Clarke stationary to the original problem and, if the additional second order nec-essary optimality conditions are satisfied, the limiting points must be M-stationary. Preliminary numerical results show that the proposed method is able to finely solve MPVCC.