Optimality Conditions for Quasi-Solutions of Vector Optimization Problems

In this paper, we deal with quasi-solutions of constrained vector optimization problems. These solutions are a kind of approximate minimal solutions and they are motivated by the Ekeland variational principle. We introduce several notions of quasi-minimality based on free disposal sets and we characterize these solutions through scalarization and Lagrange multiplier rules. When the problem fulfills certain convexity assumptions, these results are obtained by using linear separation and the Fenchel subdifferential. In the nonconvex case, they are stated by using the so-called Gerstewitz (Tammer) nonlinear separation functional and the Mordukhovich subdifferential.