SQP子问题解集的有限收敛性

Finite Convergence of the Solution Set for SQP Subproblem

序列二次规划方法(SQP)是求解约束优化问题的最有效的方法之一。SQP方法求解过程中产生的子问题是一个带参数的二次规划问题(SQP多参数规划子问题)。本文在SQP多参数规划子问题中,引入了其解集弱强的概念,讨论了弱强集的性质,并在其解集是弱强的条件下,给出了由任意算法所产生的可行解序列有限收敛的必要与充分条件。

Sequential Quadratic Programming (SQP) method is one of the most effective methods for solving constrained optimization problems. There is a class of subproblems during the process via SQP method. The subproblem which is called SQP multi-parameter subproblem is a multi-parametric quadratic programming. In this work, we introduce weak sharp solution set into SQP multi-pa- rameter subproblem. The character of weak sharp solution set is discussed. Under weak sharp conditions of solution set, the sufficient and necessary condition for finite convergence of feasible solution sequence via any algorithm is obtained.