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Minimizing Compositions of Differences-of-Convex Functions with Smooth Mappings

Author

Listed:
  • Hoai An Le Thi

    (Université de Lorraine, LGIPM, Département IA, F-57000 Metz, France; Institut Universitaire de France (IUF), 75000 Paris, France)

  • Van Ngai Huynh

    (Department of Mathematics, University of Quynhon, Qui Nhon 590000, Vietnam)

  • Tao Pham Dinh

    (Laboratory of Mathematics, INSA-Rouen, University of Normandie, 76801 Saint-Etienne-du-Rouvray Cedex, France)

Abstract

We address the so-called DC (difference-of-convex functions) composite minimization problems (or DC composite programs ) whose objective function is a composition of a DC function with a continuously differentiable mapping. We first develop an algorithm named DC composite algorithm (DCCA in short) for unconstrained DC composite programs and further extend to DC composite programs with constraints of inclusion associated with a smooth mapping and a closed convex set. The convergence analysis of the proposed algorithms is investigated. Applications of DCCA for two different problems, computation of the numerical radius of a square matrix and minimization of composite energies, are presented.

Suggested Citation

  • Hoai An Le Thi & Van Ngai Huynh & Tao Pham Dinh, 2024. "Minimizing Compositions of Differences-of-Convex Functions with Smooth Mappings," Mathematics of Operations Research, INFORMS, vol. 49(2), pages 1140-1168, May.
    • Handle: RePEc:inm:ormoor:v:49:y:2024:i:2:p:1140-1168
    DOI: 10.1287/moor.2021.0258
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