CAJ | 학술논문

互补约束优化问题是一类重要的最优化问题，在科学和工程中有着重要的应用。交通规划的道路扩容问题，经济学领域的DICE模型都是互补约束优化问题。这类问题因为约束集合不满足通常的约束规范而不能用传统的非线性规划方法处理，往往用光滑近似的方法来克服这一困难。考虑一类互补约束优化问题的基于光滑化Fischer-Burmeister 函数的扰动方法。证明了当光滑化参数μ↘0时扰动问题的值收敛到原问题的最优值，扰动问题的最优解集合的外极限包含在问题最优解集合中。说明扰动问题很容易满足通常的约束规范，并给出扰动问题的一阶必要性最优条件和二阶充分性最优条件。
호보약속우화문제시일류중요적최우화문제，재과학화공정중유착중요적응용。교통규화적도로확용문제，경제학영역적DICE모형도시호보약속우화문제。저류문제인위약속집합불만족통상적약속규범이불능용전통적비선성규화방법처리，왕왕용광활근사적방법래극복저일곤난。고필일류호보약속우화문제적기우광활화Fischer-Burmeister 함수적우동방법。증명료당광활화삼수μ↘0시우동문제적치수렴도원문제적최우치，우동문제적최우해집합적외겁한포함재문제최우해집합중。설명우동문제흔용역만족통상적약속규범，병급출우동문제적일계필요성최우조건화이계충분성최우조건。
Mathematical programs with complementarity constraints are an important class of optimi-zation problems ,which have important applications in science and engineering .For examples ,the road capacity expansion problem in transportation and the DICE model in economics are such kind of problems .Traditional nonlinear programming solvers can not be used to solve mathematical programs with complementarity constraints ,because conventional constraint qualifications do not hold for the constraint sets ,and smooth approximationmethods are proposed to overcome such a difficulty .This paper considers the perturbation approach based on the smoothed Fischer-Burmeister function for a class of optimization problems with complementarity constraints .We prove that the optimal value of the perturbed problem converges to that of the original problem and the outer limit of the solution set for the perturbed problem is contained in the solution set of the original problem w hen the smoothing parameter μ↘0 .We explain w hy the conventionally used constraint qualifications are easily satisfied and present the first-order necessary optimality conditions and the second-order sufficient optimality conditions for the perturbed problems .