Refail Kasimbeyli

Weak subgradient algorithm for solving nonsmooth nonconvex unconstrained optimization problems

  • Gulcin Dinc Yalcin
  • Refail Kasimbeyli
    • Categories Nonsmooth Optimization, Unconstrained Optimization Tags

    This paper presents a weak subgradient based method for solving nonconvex unconstrained optimization problems. The method uses a weak subgradient of the objective function at a current point, to generate a new one at every iteration. The concept of the weak subgradient is based on the idea of using supporting cones to the graph of … Read more

    Properly optimal elements in vector optimization with variable ordering structures

  • Gabriele Eichfelder
  • Refail Kasimbeyli
    • Categories Multi-Criteria Optimization, Nonlinear Optimization Tags , , ,

    In this paper, proper optimality concepts in vector optimization with variable ordering structures are introduced for the first time and characterization results via scalarizations are given. New type of scalarizing functionals are presented and their properties are discussed. The scalarization approach suggested in the paper does not require convexity and boundedness conditions. CitationPreprint of the … Read more

    A Generalization of a Theorem of Arrow, Barankin and Blackwell to a Nonconvex Case

  • Refail Kasimbeyli
  • Musa Mammadov
    • Categories Global Optimization, Global Optimization Theory, Multi-Criteria Optimization Tags , , , , , ,

    The paper presents a generalization of a known density theorem of Arrow, Barankin, and Blackwell for properly efficient points defined as support points of sets with respect to monotonically increasing sublinear functions. This result is shown to hold for nonconvex sets of a reflexive Banach space partially ordered by a Bishop–Phelps cone. CitationDepartment of Industrial … Read more