COMPUTING THE SET OF OPTIMAL POINTS FOR NONCONVEX MULTI-OBJECTIVE OPTIMIZATION PROBLEMS

Kasımbeyli R., Bulbul K. G., Soleimani B., Ozturk G.

Journal of Nonlinear and Variational Analysis, vol.10, no.4, pp.845-866, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 4
  • Publication Date: 2026
  • Doi Number: 10.23952/jnva.10.2026.4.08
  • Journal Name: Journal of Nonlinear and Variational Analysis
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.845-866
  • Keywords: Conic scalarization, Multi-objective programming, Nonconvex optimization, Pascoletti-Serafini method, Scalarization
  • Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

This paper proposes a new method for computing a set of optimal points, namely, minimal, properly minimal, and weakly minimal points, and approximate optimal points for nonconvex multi-objective problems, based on a given set of weights and reference points. This is an iterative method that utilizes the scalarizing functions of both the Conic Scalarization and the Pascoletti-Serafini methods at each iteration. The convergence of the proposed method is proven, and it is demonstrated that the method terminates in a finite number of iterations for a specified error accuracy. The performance of the method is illustrated through numerical examples.