Strict Constraint Qualifications and Sequential Optimality Conditions for Constrained Optimization
研究了约束优化中局部极小点必然满足的序列最优性条件，并定义了与之对应的严格约束条件，分析了不同严格约束条件之间的关系及其与经典约束条件的联系。
Sequential optimality conditions for constrained optimization are necessarily satisfied by local minimizers, independently of the fulfillment of constraint qualifications. These conditions support the employment of different stopping criteria for practical optimization algorithms. On the other hand, when an appropriate property on the constraints holds at a point that satisfies a sequential optimality condition, such a point also satisfies the Karush-Kuhn-Tucker conditions. Those properties will be called strict constraint qualifications in this paper. As a consequence, for each sequential optimality condition, it is natural to ask for its weakest strict associated constraint qualification. This problem has been solved in a recent paper for the Approximate Karush-Kuhn-Tucker sequential optimality condition. In the present paper, we characterize the weakest strict constraint qualifications associated with other sequential optimality conditions that are useful for defining stopping criteria of algorithms. In addition, we prove all the implications between the new strict constraint qualifications and other (classical or strict) constraint qualifications.