Optimality conditions for (h, φ)-subdifferentiable multiobjective programming problems with G-type I functions

  • Tadeusz Antczak
  • Vinay Singh NIT Mizoram
  • Solomon Lalmalsawma
Keywords: (h,φ)-subdifferentiable multiobjective programming problem, optimality conditions, weak Pareto solution, (h, φ)-subdifferentiable vector Mond-Weir dual problem, (h, φ)-G-type I functions

Abstract

In this paper, using generalized algebraic operations introduced by Ben-Tal [7], we introduce new classes of (h,φ)-subdifferentiable functions, called (h,φ)-G-type I functions and generalized (h,φ)-G-type I functions. Then, we consider a class of nonconvex (h, φ)-subdifferentiable multiobjective programming problems with locally Lipschitz functions in which the functions involved belong to aforesaid classes of (h, φ)-subdifferentiable nonconvex functions. For such (h, φ)-subdifferentiable vector optimization problems, we prove the sufficient optimality conditions for a feasible solution to be its (weak) Pareto solution. Further, we define a vector dual problem in the sense of Mond-Weir for the considered (h, φ)-subdifferentiable multiobjective programming problem and we prove several duality theorems for the aforesaid (h, φ)-subdifferentiable vector optimization problems also under (h, φ)-G-type I hypotheses.
Published
2024-04-13
How to Cite
Antczak, T., Singh, V., & Lalmalsawma, S. (2024). Optimality conditions for (h, φ)-subdifferentiable multiobjective programming problems with G-type I functions. Statistics, Optimization & Information Computing, 12(4), 1103-1122. https://doi.org/10.19139/soic-2310-5070-1930
Section
Research Articles