A sharp augmented Lagrangian-based method in constrained non-convex optimization

Bagirov A. M., Ozturk G., Kasimbeyli R.

OPTIMIZATION METHODS & SOFTWARE, vol.34, no.3, pp.462-488, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 34 Issue: 3
  • Publication Date: 2019
  • Doi Number: 10.1080/10556788.2018.1496431
  • Journal Name: OPTIMIZATION METHODS & SOFTWARE
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.462-488
  • Keywords: Constrained optimization, non-convex optimization, non-smooth optimization, sharp augmented Lagrangian, discrete gradient method, modified subgradient algorithm, MODIFIED SUBGRADIENT ALGORITHM, RADIAL EPIDERIVATIVES, GENERAL CONSTRAINTS, BUNDLE METHOD, DUALITY
  • Anadolu University Affiliated: Yes

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.