On Approximate Solutions in Convex Vector Optimization
Sien Deng · SIAM Journal on Control and Optimization · 1997
Necessary and sufficient conditions are obtained for the existence of $\epsilon$-weak minima for constrained convex vector optimization problems. The characterization of $\epsilon$-weak minima is given in terms of $\epsilon$-optimal solutions of the associated scalar optimization problems and $\epsilon$-directional derivatives of objective functions. The Lipschitzian continuity of $\epsilon$-weak minima is proved under mild conditions.