An implementation of a reduced subgradient method via Luenberger-Mokhtar variant. (2nd July 2016)

• Record Type: Journal Article
• Authors: El Ghali, A.; El Moudden, M.
• Is Part Of: Optimization. Volume 65:Number 7(2016)
• Page Start: 1497
• Page End: 1518
• Publication Date: 2016-07-02
• Subjects: Mathematical programming -- nondifferentiable convex optimization -- linearly constrained minimization -- reduced subgradient algorithm -- bundle methods; 90C52 -- 65K05; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1147037
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : We present an implementable algorithm for minimizing a convex function which is not necessarily differentiable subject to linear equality constraints and to nonnegativity bounds on the variables. The algorithm is based on extending the variant proposed by Luenberger to the nondifferentiable case and using the bundle techniques introduced by Lemaréchal to approximate the subdifferential of the objective function. In particular, at each iteration, we compute a search direction by solving a quadratic subproblem, and an inexact line search along this direction yields a decrease in the objective value. Under some assumptions, the convergence of the proposed algorithm is analysed. Finally, some numerical results are presented, which show that the algorithm performs efficiently.