论文标题
分段线性界面复合材料优化中SQP方法的原始超级线性收敛性
Primal superlinear convergence of SQP methods in piecewise linear-quadratic composite optimization
论文作者
论文摘要
本文主要涉及准牛顿顺序二次编程（SQP）方法的原始超值收敛，用于分段线性 - 季度复合优化问题。我们表明，在拉格朗日倍增器的非批评性和丹尼斯摩尔条件的版本下，后者的原始超级线性融合可以是合理的。此外，我们表明，如果我们用二阶足够条件替换非临界条件，那么这种原始的超级线性收敛等于丹尼斯 - 摩尔条件的适当版本。我们还为基本SQP方法的原始二重性超线性恢复了Bonnans的结果，以在二阶足够条件和Lagrange乘数的唯一性下为此类别的复合问题。为了实现这些目标，我们首先获得了凸面分段线性季节功能的还原引理的扩展，然后对Lagrange乘数的非关键性进行了全面分析，以解决复合问题。我们还为复合问题的KKT系统建立了一定的原始估计，这些估计在我们对准Newton SQP方法的局部收敛分析中起着重要作用。
This paper mainly concerns with the primal superlinear convergence of the quasi-Newton sequential quadratic programming (SQP) method for piecewise linear-quadratic composite optimization problems. We show that the latter primal superlinear convergence can be justified under the noncriticality of Lagrange multipliers and a version of the Dennis-More condition. Furthermore, we show that if we replace the noncriticality condition with the second-order sufficient condition, this primal superlinear convergence is equivalent with an appropriate version of the Dennis-More condition. We also recover Bonnans' result in [1] for the primal-dual superlinear of the basic SQP method for this class of composite problems under the second-order sufficient condition and the uniqueness of Lagrange multipliers. To achieve these goals, we first obtain an extension of the reduction lemma for convex Piecewise linear-quadratic functions and then provide a comprehensive analysis of the noncriticality of Lagrange multipliers for composite problems. We also establish certain primal estimates for KKT systems of composite problems, which play a significant role in our local convergence analysis of the quasi-Newton SQP method.
