Proximal-gradient algorithms for fractional programming. (3rd August 2017)

• Record Type: Journal Article
• Authors: Boţ, Radu Ioan; Csetnek, Ernö Robert
• Is Part Of: Optimization. Volume 66:Number 8(2017)
• Page Start: 1383
• Page End: 1396
• Publication Date: 2017-08-03
• Subjects: Fractional programming -- forward–backward algorithm -- convergence rate -- convex subdifferential -- limiting subdifferential -- Kurdyka-ᴌojasiewicz property; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1294592
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we propose two proximal-gradient algorithms for fractional programming problems in real Hilbert spaces, where the numerator is a proper, convex and lower semicontinuous function and the denominator is a smooth function, either concave or convex. In the iterative schemes, we perform a proximal step with respect to the nonsmooth numerator and a gradient step with respect to the smooth denominator. The algorithm in case of a concave denominator has the particularity that it generates sequences which approach both the (global) optimal solutions set and the optimal objective value of the underlying fractional programming problem. In case of a convex denominator the numerical scheme approaches the set of critical points of the objective function, provided the latter satisfies the Kurdyka-ᴌojasiewicz property.