约束优化问题的序列近似方法收敛性

对抽象约束优化问题的序列近似方法的收敛性进行讨论,证明了在目标函数序列连续收敛和约束集合序列收敛的条件下,序列近似问题的全局最优值收敛到原问题的最优值.进一步,证明了在序列近似问题目标函数和约束集合具有某些单调性质的前提下,把目标函数序列连续收敛减弱到上图收敛,该结论仍然成立.最后,将这一结果用于分析互补约束优化问题的光滑化方法的收敛性中.

Convergence of sequential approximation method for constrained optimization problems

The convergence of the sequential approximation method for abstract constrained optimization problems is discussed. It is proved that the global optimal solutions of the sequential approximation problems converge to the optimal solutions of the original problem under the continuous convergency of the objective function sequence and the convergency of the constrained set sequence. Moreover, if the objective function sequence is assumed to be epi-convergence instead of continuous convergence, the conclusion still holds when some monotonicity property of the objective functions and the constrained sets of the sequential approximation problems is satisfied. At last, the research result can be applied to analyze the convergence of the smoothing method in solving complementarity constraint optimization problem.