2020/07/13 by Ebrahim Sarabi, Sarabi, Ebrahim
Computer Science · Engineering · Mathematics · #49J52 #49J53 #65K99 #90C31 #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #PAPR reduction in OFDM #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.2007.06187
openalex publication_date 2020/07/13 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
This paper mainly concerns with the primal superlinear convergence of the\nquasi-Newton sequential quadratic programming (SQP) method for piecewise\nlinear-quadratic composite optimization problems. We show that the latter\nprimal superlinear convergence can be justified under the noncriticality of\nLagrange multipliers and a version of the Dennis-More condition. Furthermore,\nwe show that if we replace the noncriticality condition with the second-order\nsufficient condition, this primal superlinear convergence is equivalent with an\nappropriate version of the Dennis-More condition. We also recover Bonnans'\nresult in [1] for the primal-dual superlinear of the basic SQP method for this\nclass of composite problems under the second-order sufficient condition and the\nuniqueness of Lagrange multipliers. To achieve these goals, we first obtain an\nextension of the reduction lemma for convex Piecewise linear-quadratic\nfunctions and then provide a comprehensive analysis of the noncriticality of\nLagrange multipliers for composite problems. We also establish certain primal\nestimates for KKT systems of composite problems, which play a significant role\nin our local convergence analysis of the quasi-Newton SQP method.\n