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Journal Articles Journal of Optimization Theory and Applications Year : 2018

Conditional Gradient Method for Double-Convex Fractional Programming Matrix Problems

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Abstract

We consider the problem of optimizing the ratio of two convex functions over a closed and convex set in the space of matrices. This problem appears in several applications and can be classified as a double-convex fractional programming problem. In general, the objective function is nonconvex but, nevertheless, the problem has some special features. Taking advantage of these features, a conditional gradient method is proposed and analyzed, which is suitable for matrix problems. The proposed scheme is applied to two different specific problems, including the well-known trace ratio optimization problem which arises in many engineering and data processing applications. Preliminary numerical experiments are presented to illustrate the properties of the proposed scheme.
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Dates and versions

hal-03135657 , version 1 (09-02-2021)

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Abderrahman Bouhamidi, Mohammed Bellalij, Rentsen Enkhbat, Khalide Jbilou, Marcos Raydan. Conditional Gradient Method for Double-Convex Fractional Programming Matrix Problems. Journal of Optimization Theory and Applications, 2018, 176 (1), pp.163-177. ⟨10.1007/s10957-017-1203-3⟩. ⟨hal-03135657⟩
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