A sharp augmented Lagrangian-based method in constrained non-convex optimization. (4th May 2019)

• Record Type: Journal Article
• Authors: Bagirov, A. M.; Ozturk, G.; Kasimbeyli, R.
• Is Part Of: Optimization methods and software. Volume 34:Number 3(2019)
• Page Start: 462
• Page End: 488
• Publication Date: 2019-05-04
• Subjects: Constrained optimization -- non-convex optimization -- non-smooth optimization -- sharp augmented Lagrangian -- discrete gradient method -- modified subgradient algorithm; 65K05 -- 90C25; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2018.1496431
• Languages: English
• ISSNs: 1055-6788

Abstract

ABSTRACT: In this paper, a novel sharp Augmented Lagrangian-based global optimization method is developed for solving constrained non-convex optimization problems. The algorithm consists of outer and inner loops. At each inner iteration, the discrete gradient method is applied to minimize the sharp augmented Lagrangian function. Depending on the solution found the algorithm stops or updates the dual variables in the inner loop, or updates the upper or lower bounds by going to the outer loop. The convergence results for the proposed method are presented. The performance of the method is demonstrated using a wide range of nonlinear smooth and non-smooth constrained optimization test problems from the literature.