中文摘要：

均衡约束优化问题在经济领域有着广泛的应用。研究了一类非线性互补约束均衡问题的可行性条件,其中约束条件不仅含有互补约束,而且还含有包括第一水平变量和第二水平变量的非线性约束,给出了两个新的假设,进而推广了线性互补约束优化问题的可行性条件。在一定条件下,分别证明了非线性互补约束的均衡问题是可行的和一类均衡问题中的SQP算法子问题的可行域非空。

英文摘要：

Mathematical programs with equilibrium constraints （MPEC for short ） is widely applied in economic field. Feasibility conditions on a class of mathematical programs with nonlinear complementarity equilibrium constraints are considered, where the constraints not only include complementarity constraints, but also nonlinear constraints presented by the first level and the second level variables. Two new assumptions are given, and further, the feasibility conditions for the mathematical program with linear complementarity equilibrium constraints are extend- ed. Under some appropriate assumptions, it is shown that the mathematical programs with nonlinear equilibrium complementarity constraints are feasible and the sub-problems of SQP algorithm for a class of MPEC can be consistent respectively.