4.1 Article

An approach to characterizing ε-solution sets of convex programs

Journal

TOP
Volume 30, Issue 2, Pages 249-269

Publisher

SPRINGER
DOI: 10.1007/s11750-021-00616-y

Keywords

epsilon-solution; epsilon-solution set; Minimizing sequence; epsilon-Kuhn-Tucker vector

Funding

  1. Vietnam Ministry of Education and Training [B2021-SP2-06]
  2. Research Center for Nonlinear Analysis and Optimization Kaohsiung Medical University, Taiwan
  3. Saigon University
  4. VIASM
  5. [MOST 108-2115-M-037-001]

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This paper proposes an approach to characterize epsilon-solution sets of convex programs with a given epsilon > 0, divided into two parts. The first part establishes the expressions of epsilon-solution sets of a class of convex infinite programs, while the second part focuses on some special cases, such as the epsilon-solution sets of convex programs with set constraints. The results are validated through several examples.
In this paper, we propose an approach to characterizing epsilon-solution sets of convex programs with a given epsilon > 0. The results are divided into two parts. The first one is devoted to establishing the expressions of epsilon-solution sets of a class of convex infinite programs. The representation is given based on the study of relationships among the following three sets: the set of Lagrange multipliers corresponding to a given epsilon-solution, the set of epsilon-solutions of the dual problem corresponding, and the set of epsilon-Kuhn-Tucker vectors associated with the problem in consideration. The second one is devoted to some special cases: the epsilon-solution sets of convex programs that have set constraints and the almost epsilon-solution sets of convex programs that have finite convex constraints. Several examples are given.

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