On Solution of One Equation with d.c. Function

Article type: Research Article

Authors: Strekalovskiy, Alexander^{1; *} | Musatova, Elena²

Affiliations: [1] Matrosov Institute for System Dynamics & Control Theory SB RAS, Lermontov St., 134, Irkutsk, 664033, Russia. E-mail: [email protected] | [2] V.A. Trapeznikov Institute of Control Sciences of RAS, Profsoyuznaya St., 65, Moscow, 117997, Russia. E-mail: [email protected]

Correspondence: [*] Corresponding author.

Abstract: In the paper we address the classical problem of solving one equation given by (d.c.) function represented by the difference of two convex functions. This problem is initiated by the optimization problems with constraints in the form of inequalities and/or equalities given by d.c. functions when one needs to descent from an unfeasible point to the boundary of a constraint improving, at the same time, the value of the objective function. We propose a new numerical procedure which allows to do this. Further, for the developed algorithm we provide the convergence results and numerical results of computational testing which look rather promising and competitive.

Keywords: d.c. functions, nonlinear equation, numerical method, nonconvex optimization

Journal: Informatica, vol. 27, no. 2, pp. 367-386, 2016