Counterexample and optimality conditions in differentiable multiobjective programming

Authors
Kim, DS Lee, GM Lee, BS Cho, SJ
Citation
Ds. Kim et al., Counterexample and optimality conditions in differentiable multiobjective programming, J OPTIM TH, 109(1), 2001, pp. 187-192
Citations number
3
Categorie Soggetti
Engineering Mathematics
Journal title
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
ISSN journal
00223239 → ACNP
Volume
109
Issue
1
Year of publication
2001
Pages
187 - 192
Database
ISI
SICI code
0022-3239(200104)109:1<187:CAOCID>2.0.ZU;2-T
Abstract
Recently, sufficient optimality theorems for (weak) Pareto-optimal solution s of a multiobjective optimization problem (MOP) were stated in Theorems 3. 1 and 3.3 of Ref. 1. In this note, we give a counterexample showing that th e theorems of Ref. 1 are not true. Then, by modifying the assumptions of th ese theorems, we establish two new sufficient optimality theorems for (weak ) Pareto-optimal solutions of (MOP); moreover, we give generalized sufficie nt optimality theorems for (MOP).