ALESQP: An Augmented Lagrangian Equality-Constrained SQP Method for Optimization with General Constraints

Antil, Harbir; Kouri, Drew Philip; Ridzal, Denis

doi:10.1137/20m1378399

Title: ALESQP: An Augmented Lagrangian Equality-Constrained SQP Method for Optimization with General Constraints

Journal Article · Tue Nov 21 00:00:00 EST 2023 · SIAM Journal on Optimization

DOI:https://doi.org/10.1137/20m1378399· OSTI ID:2311683

^[1];

^[2]; Ridzal, Denis ^[2]

George Mason University, Fairfax, VA (United States)
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Here we present a new algorithm for infinite-dimensional optimization with general constraints, called ALESQP. In short, ALESQP is an augmented Lagrangian method that penalizes inequality constraints and solves equality-constrained nonlinear optimization subproblems at every iteration. The subproblems are solved using a matrix-free trust-region sequential quadratic programming (SQP) method that takes advantage of iterative, i.e., inexact linear solvers, and is suitable for large-scale applications. A key feature of ALESQP is a constraint decomposition strategy that allows it to exploit problem-specific variable scalings and inner products. We analyze convergence of ALESQP under different assumptions. We show that strong accumulation points are stationary. Consequently, in finite dimensions ALESQP converges to a stationary point. In infinite dimensions we establish that weak accumulation points are feasible in many practical situations. Under additional assumptions we show that weak accumulation points are stationary. We present several infinite-dimensional examples where ALESQP shows remarkable discretization-independent performance in all of its iterative components, requiring a modest number of iterations to meet constraint tolerances at the level of machine precision. Also, we demonstrate a fully matrix-free solution of an infinite-dimensional problem with nonlinear inequality constraints.

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Research Organization:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF); US Air Force Office of Scientific Research (AFOSR); USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: NA0003525; DMS-2110263; DMS- 1913004; FA9550-19-1-0036; FA9550-22-1-0248; F4FGA09135G001

OSTI ID:: 2311683

Report Number(s):: SAND-2023-12921J

Journal Information:: SIAM Journal on Optimization, Vol. 33, Issue 1; ISSN 1052-6234

Publisher:: Society for Industrial and Applied Mathematics (SIAM)Copyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
ALESQP
augmented Lagrangian
composite step trust-region method
SQQP
convergence analysis
constraint decomposition
nonlinear constraints

Title: ALESQP: An Augmented Lagrangian Equality-Constrained SQP Method for Optimization with General Constraints

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