On Approximate Solutions in Convex Vector Optimization

Authors:
Sien Deng
Affiliations:
-
Venue:
SIAM Journal on Control and Optimization
Year:
1997

Citing 0
Cited 3

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Some properties of approximate solutions for vector optimization problem with set-valued functions

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A generic approach to approximate efficiency and applications to vector optimization with set-valued maps

Journal of Global Optimization

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Abstract

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.