Abstract
Based on the concepts introduced in the preceding chapters we now present optimality conditions for set optimization problems. These conditions are discussed using contingent epiderivatives, subgradients and weak subgradients. The main section of this chapter is devoted to a generalization of the Lagrange multiplier rule. We present this multiplier rule as a necessary optimality condition. Assumptions ensuring that this multiplier rule is a sufficient optimality condition are also given.
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© 2011 Springer-Verlag Berlin Heidelberg
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Jahn, J. (2011). Optimality Conditions. In: Vector Optimization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17005-8_17
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DOI: https://doi.org/10.1007/978-3-642-17005-8_17
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17004-1
Online ISBN: 978-3-642-17005-8
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