不等式约束极大极小问题的一个新型模松弛强次可行SQCQP算法

针对带不等式约束的极大极小问题,借鉴一般约束优化问题的模松弛强次可行SQP算法思想,提出了求解不等式约束极大极小问题的一个新型模松弛强次可行SQCQP算法.首先,通过在QCQP子问题中选取合适的罚函数,保证了算法的可行性以及目标函数F(x)的下降性,同时简化QCQP子问题二次约束项参数α_k的选取,可保证算法的可行性和收敛性.其次,算法步长的选取合理简单.最后,在适当的假设条件下证明了算法具有全局收敛性及强收敛性.初步的数值试验结果表明算法是可行有效的.

A STRONGLY SUB-FEASIBLE NORM-RELAXED SQCQP ALGORITHM FOR THE INEQUALITY CONSTRAINED MINIMAX PROBLEMS

In this paper, the minimax problems with inequality constraints are discussed, and a new strongly sub-feasible norm-relaxed SQCQP algorithm for the inequality constrained minimax problems is proposed. First, the penalty function $a_k$ in the QCQP subproblem can ensure the feasibility of the algorithm and the descent property of the objective function F(x), and the parameter α_k of quadratic constraints can guarantee the feasibility and convergence of the algorithm. Second, the determination of stepsize is reasonable and simple. Finally,the proposed algorithm possesses global convergence under suitable assumptions. The preliminary numerical experiments show that the algorithm is feasible and effective.