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Conditional Gradient Method for Double-Convex Fractional Programming Matrix Problems

Author

Listed:
  • Abderrahman Bouhamidi

    (Université du Littoral Côte d’Opale)

  • Mohammed Bellalij

    (Université de Valenciennes)

  • Rentsen Enkhbat

    (National University of Mongolia)

  • Khalid Jbilou

    (Université du Littoral Côte d’Opale)

  • Marcos Raydan

    (Universidad Simón Bolívar)

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.

Suggested Citation

  • Abderrahman Bouhamidi & Mohammed Bellalij & Rentsen Enkhbat & Khalid Jbilou & Marcos Raydan, 2018. "Conditional Gradient Method for Double-Convex Fractional Programming Matrix Problems," Journal of Optimization Theory and Applications, Springer, vol. 176(1), pages 163-177, January.
    • Handle: RePEc:spr:joptap:v:176:y:2018:i:1:d:10.1007_s10957-017-1203-3
    DOI: 10.1007/s10957-017-1203-3
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    References listed on IDEAS

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    1. Schaible, Siegfried & Ibaraki, Toshidide, 1983. "Fractional programming," European Journal of Operational Research, Elsevier, vol. 12(4), pages 325-338, April.
    2. Z. A. Liang & H. X. Huang & P. M. Pardalos, 2001. "Optimality Conditions and Duality for a Class of Nonlinear Fractional Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 110(3), pages 611-619, September.
    3. Schaible, Siegfried, 1981. "Fractional programming: Applications and algorithms," European Journal of Operational Research, Elsevier, vol. 7(2), pages 111-120, June.
    4. Werner Dinkelbach, 1967. "On Nonlinear Fractional Programming," Management Science, INFORMS, vol. 13(7), pages 492-498, March.
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    Cited by:

    1. Oumaima Benchettou & Abdeslem Hafid Bentbib & Abderrahman Bouhamidi, 2023. "An Accelerated Tensorial Double Proximal Gradient Method for Total Variation Regularization Problem," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 111-134, July.

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