Accelerating convergence of a globalized sequential quadratic programming method to critical Lagrange multipliers

• Published in: Computational optimization and applications Vol. 80; no. 3; pp. 943 - 978
• Main Author: Izmailov, A. F.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01-12-2021; Springer Nature B.V
• Subjects: Algorithms; Asymptotic methods; Constraints; Convergence; Convex and Discrete Geometry; Lagrange multiplier; Management Science; Mathematics; Mathematics and Statistics; Operations Research; Operations Research/Decision Theory; Optimization; Penalty function; Quadratic programming; Statistics; 65K05; Equality-constrained optimization; Unit stepsize; Merit function; Lagrange optimality system; Critical Lagrange multiplier; 2-regularity; extrapolation; 90C30; Sequential quadratic programming; 90C55; Newton-type methods; Nonsmooth exact penalty function; 65K10; 49M05; Linesearch globalization of convergence; True Hessian; 49M15
• ISSN: 0926-6003; 1573-2894
• DOI: 10.1007/s10589-021-00317-z

This paper concerns the issue of asymptotic acceptance of the true Hessian and the full step by the sequential quadratic programming algorithm for equality-constrained optimization problems. In order to enforce global convergence, the algorithm is equipped with a standard Armijo linesearch procedure for a nonsmooth exact penalty function. The specificity of considerations here is that the standard assumptions for local superlinear convergence of the method may be violated. The analysis focuses on the case when there exist critical Lagrange multipliers, and does not require regularity assumptions on the constraints or satisfaction of second-order sufficient optimality conditions. The results provide a basis for application of known acceleration techniques, such as extrapolation, and allow the formulation of algorithms that can outperform the standard SQP with BFGS approximations of the Hessian on problems with degenerate constraints. This claim is confirmed by some numerical experiments.