Proximal-gradient algorithms for fractional programming

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...

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Bibliographic Details
Published in:Optimization Vol. 66; no. 8; pp. 1383 - 1396
Main Authors: Boţ, Radu Ioan, Csetnek, Ernö Robert
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis 03.08.2017
Taylor & Francis LLC
Subjects:
Algorithms
convergence rate
convex subdifferential
forward-backward algorithm
Fractional programming
Iterative methods
Kurdyka-ᴌojasiewicz property
limiting subdifferential
Mathematical programming
Programming
ISSN:0233-1934, 1029-4945, 1029-4945
Online Access:Get full text
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Summary: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.
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ISSN:0233-1934
1029-4945
1029-4945
DOI:10.1080/02331934.2017.1294592