Iteration Complexity of a Proximal Augmented Lagrangian Method for Solving Nonconvex Composite Optimization Problems with Nonlinear Convex Constraints

Weiwei Kong (), Jefferson G. Melo () and Renato D. C. Monteiro ()
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Weiwei Kong: Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830
Jefferson G. Melo: Instituto de Matemática e Estatística, Universidade Federal de Goiás, Goiânia, Goiás 74001-970, Brazil
Renato D. C. Monteiro: School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332

Mathematics of Operations Research, 2023, vol. 48, issue 2, 1066-1094

Abstract: This paper proposes and analyzes a proximal augmented Lagrangian (NL-IAPIAL) method for solving constrained nonconvex composite optimization problems, where the constraints are smooth and convex with respect to the order given by a closed convex cone. Each NL-IAPIAL iteration consists of inexactly solving a proximal augmented Lagrangian subproblem by an accelerated composite gradient method followed by a Lagrange multiplier update. Under some mild assumptions, a complexity bound for NL-IAPIAL to obtain an approximate stationary solution of the problem is also derived. Numerical experiments are also given to illustrate the computational efficiency of the proposed method.

Keywords: Primary: 9M05; 49M37; 90C26; 90C30; 90C60; 65K05; 65K10; 68Q25; 65Y20; inexact proximal augmented Lagrangian method; K -convexity; nonlinear constrained smooth nonconvex composite programming; accelerated first-order methods; iteration complexity (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:48:y:2023:i:2:p:1066-1094

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