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

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...

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Vydáno v:Computational optimization and applications Ročník 80; číslo 3; s. 943 - 978
Hlavní autor: Izmailov, A. F.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.12.2021
Springer Nature B.V
Témata:
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
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Popis
Shrnutí: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.
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-021-00317-z