ϵ-Optimality Criteria for Vector Minimization Problems via Exact Penalty Functions

Several authors have been interested in ϵ-optimality criteria for scalar programming problems. In this paper, some ϵ-optimality results for the scalar problems of ours [Math. Programming56 (1992), 233-243] are extended to vector minimization problems via exact penalty functions. Similar to our paper, the solvability of neither the vector problems nor the associated dual problems is assumed. Our criteria are derived by estimating the size of the penalty parameter in terms of ϵ-approximate solutions for the dual problems.