Q-subdifferential and Q-conjugate for global optimality |
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Authors: | D Fortin I Tseveendorj |
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Institution: | 1. Domaine de Voluceau, Rocquencourt, INRIA, B.P. 105, 78153, Le Chesnay Cedex, France 2. Laboratoire PRiSM, UMR 8144 Université de Versailles 45, avenue des états-Unis, 78035, Versailles Cedex, France
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Abstract: | Normal cone and subdifferential have been generalized through various continuous functions; in this article, we focus on a non separable Q-subdifferential version. Necessary and sufficient optimality conditions for unconstrained nonconvex problems are revisited accordingly. For inequality constrained problems, Q-subdifferential and the lagrangian multipliers, enhanced as continuous functions instead of scalars, allow us to derive new necessary and sufficient optimality conditions. In the same way, the Legendre-Fenchel conjugate is generalized into Q-conjugate and global optimality conditions are derived by Q-conjugate as well, leading to a tighter inequality. |
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