半代数规划和Tame规划的优化-极小化过程和SQP方法的收敛性
Majorization-minimization procedures and convergence of SQP methods for semi-algebraic and tame programs
摘要：
鉴于解决涉及复杂约束的非光滑和非凸问题（如标准NLP问题），我们研究了由强凸子问题族产生的一般最大化-最小化过程。利用半代数几何和变分分析的技巧--特别是Lojasiewicz不等式--我们建立了由这类方案产生的序列到临界点的收敛性。这个过程的广泛适用性在NLP的背景下说明。在这种情况下，临界点与KKT点重合。当数据是半代数或真正的分析，我们的方法适用于（例如）各种SQP方法的研究：移动球的方法，SL 1 QP，ESQP。在标准条件下，这提供了-据我们所知-第一个一般的收敛结果一般非线性规划问题。我们强调的事实是，与大多数关于这个问题的作品，没有二阶假设和/或凸性假设。收敛速率与一阶方法中常见的收敛速度具有相同的形式。
英文摘要：
In view of solving nonsmooth and nonconvex problems involving complex constraints (like standard NLP problems), we study general maximization-minimization procedures produced by families of strongly convex sub-problems. Using techniques from semi-algebraic geometry and variational analysis -in particular Lojasiewicz inequality- we establish the convergence of sequences generated by this type of schemes to critical points. The broad applicability of this process is illustrated in the context of NLP. In that case critical points coincide with KKT points. When the data are semi-algebraic or real analytic our method applies (for instance) to the study of various SQP methods: the moving balls method, Sl1QP, ESQP. Under standard qualification conditions, this provides -to the best of our knowledge- the first general convergence results for general nonlinear programming problems. We emphasize the fact that, unlike most works on this subject, no second-order assumption and/or convexity assumptions whatsoever are made. Rate of convergence are shown to be of the same form as those commonly encountered with first order methods.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
