Quadratic convergence of an SQP method for some optimization problems with applications to control theory

2025/05/28 by Casas, Eduardo, Mateos, Mariano
#35Q93 #49M05 #49M15 #49M41 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2505.22750

Abstract

We analyze a sequential quadratic programming algorithm for solving a class of abstract optimization problems. Assuming that the initial point is in an L² neighborhood of a local solution that satisfies no-gap second-order sufficient optimality conditions and a strict complementarity condition, we obtain stability and quadratic convergence in L^q for all q∈[p,∞] where p≥ 2 depends on the problem. Many of the usual optimal control problems of partial differential equations fit into this abstract formulation. Some examples are given in the paper. Finally, a computational comparison with other versions of the SQP method is presented.

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