Journal of Optimization Theory and Applications

, Volume 176, Issue 1, pp 163–177 | Cite as

Conditional Gradient Method for Double-Convex Fractional Programming Matrix Problems

  • Abderrahman Bouhamidi
  • Mohammed Bellalij
  • Rentsen Enkhbat
  • Khalid Jbilou
  • Marcos Raydan


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.


Fractional programming Conditional gradient method Trace ratio problem 

Mathematics Subject Classification

65F10 15A18 90C32 



We are grateful to the referees for their helpful comments and suggestions. The fifth author would like to thank Abderrahman Bouhamidi, Khalide Jbilou, and Hassane Sadok for their hospitality during a one-month visit to the Laboratory LMPA at Université du Littoral Côte d’Opale, Calais, France, in June 2017.


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Authors and Affiliations

  1. 1.Université du Littoral Côte d’OpaleCalais CedexFrance
  2. 2.Laboratoire de Mathématiques et Leurs ApplicationsUniversité de ValenciennesValenciennes CedexFrance
  3. 3.National University of MongoliaUlaanbaatarMongolia
  4. 4.Departamento de Cómputo Científico y EstadísticaUniversidad Simón BolívarCaracasVenezuela

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