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Conditional Gradient Method for Double-Convex Fractional Programming Matrix Problems

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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https://hal-uphf.archives-ouvertes.fr/hal-03135657
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Submitted on : Tuesday, February 9, 2021 - 10:39:00 AM
Last modification on : Tuesday, October 19, 2021 - 3:07:25 PM

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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, Springer Verlag, 2018, 176 (1), pp.163-177. ⟨10.1007/s10957-017-1203-3⟩. ⟨hal-03135657⟩

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