An approach to characterizing €‑solution sets of convex programs

N. V. Tuyen ^[3] ; C.F. Wen ^[1] ; T. Q. Son ^[2]
1. [1] Kaohsiung Medical University
  
  Kaohsiung Medical University
  
  Taiwán
2. [2] Saigon University
  
  Saigon University
  
  Vietnam
3. [3] Hanoi Pedagogical University 2, Vietnam
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Localización: Top, ISSN-e 1863-8279, ISSN 1134-5764, Vol. 30, Nº. 2, 2022, págs. 249-269
Idioma: inglés
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Resumen
- In this paper, we propose an approach to characterizing 휖-solution sets of convex programs with a given � > 0. The results are divided into two parts. The frst one is devoted to establishing the expressions of 휖-solution sets of a class of convex infnite 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 휖 -solution, the set of 휖-solutions of the dual problem corresponding, and the set of 휖 -Kuhn–Tucker vectors associated with the problem in consideration. The second one is devoted to some special cases: the 휖-solution sets of convex programs that have set constraints and the almost 휖-solution sets of convex programs that have fnite convex constraints. Several examples are given.