中文摘要：

文章提出了一种求解带等式与不等式约束的minimax问题的既无罚函数又无滤子的SQP算法。首先引入了ε-积极约束集,在此基础上建立了两个新的二次规划子问题得到搜索方向,既克服了Maratos效应,又大大地减少了算法的运算量;另外给出了一种新的线性搜索步长策略,该方法既避免了罚因子的选取,又减小了计算机储存量;在适当的假设条件下,证明了算法的全局收敛性;初步数值实验验证了算法的有效性与优越性。

英文摘要：

A SQP algorithm without a penalty function or a filter is introduced to solve minimax problems with equality and inequality constraints.Based on theε-active constraint subset,two new quadratic programming subproblems are established to get the search direction,which both overcomes the Maratos effect,and greatly reduces the computational complexity of the algorithm.A new linear search step length strategy is proposed,the method not only avoids a choice of penalty factor,but also reduces the storage capacity of the computer.It is proved that under appropriate assumptions,the algorithm is globally convergent;moreover,several numerical examples are reported to verify the effectiveness and superiority of the algorithm.