A Tikhonov regularization parameter approach for solving Lagrange constrained optimization problems. Issue 11 (2nd November 2018)

• Record Type: Journal Article
• Authors: Clempner, Julio B.; Poznyak, Alexander S.
• Is Part Of: Engineering optimization. Volume 50:Issue 11(2018)
• Page Start: 1996
• Page End: 2012
• Publication Date: 2018-11-02
• Subjects: Lagrange method -- optimization -- regularization -- Tikhonov; Engineering design -- Periodicals; Mathematical optimization -- Periodicals; 620.0042
• DOI: 10.1080/0305215X.2017.1418866
• Languages: English
• ISSNs: 0305-215X

Abstract

ABSTRACT: This article deals with the Tikhonov regularization method for the constrained Lagrange approach, taking into account polylinear programming problems. A regularized Lagrange function is strongly convex when having a unique saddle-point on z, and it is strongly concave on the Lagrange multipliers for any . The parameters α and δ are positive, ensuring the strong convexity and the existence of a unique solution. Herein, it is proven that, given, if then the original problem converges to a unique solution with the minimal weighted norm. A projection-gradient method for finding the extremal points is proposed, and the convergence of the proposed projection-gradient method under mild conditions is established. The rate of convergence of the parameters is shown. A numerical example related to Markov games and a second example related to signal control show the efficacy and efficiency of the proposed method.