Sequential Lagrange multiplier condition for ϵ-optimal solution in convex programming

Abstract

In the paper by Jeyakumar et al. (J. Global Optim. (2006) 36: pp. 127–137), a sequential Lagrange multiplier condition for exact optimal solutions of a general convex programming was obtained, and as a byproduct, a new constraint qualification for an exact optimal solution of the convex programming problem to satisfy the standard Lagrange multiplier condition was also obtained. In this article, we extend these results to ϵ-optimal solutions of the convex programming problem. The new constraint qualification for ϵ-optimal solutions to satisfy a Lagrange multiplier condition is therefore weaker than the Slater-type condition proposed in the paper by Strofiot et al. (Math. Program. (1983) 25: pp. 307–328).