On coderivatives and Lipschitzian properties of the dual pair in optimization |
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| Authors: | Marco A López Andrea B Ridolfi Virginia N Vera de Serio |
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| Institution: | a Department of Statistics and Operations Research, University of Alicante, Spainb Honorary Research Fellow in the Graduate School of Information Technology and Mathematical Sciences at University of Ballarat, Australiac CONICET; Faculty of Sciences Applied to Industry, National University of Cuyo, Mendoza, Argentinad Faculty of Economics and I.C.B., National University of Cuyo, Mendoza, Argentina |
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| Abstract: | In this paper, we apply the concept of coderivative and other tools from the generalized differentiation theory for set-valued mappings to study the stability of the feasible sets of both the primal and the dual problem in infinite-dimensional linear optimization with infinitely many explicit constraints and an additional conic constraint. After providing some specific duality results for our dual pair, we study the Lipschitz-like property of both mappings and also give bounds for the associated Lipschitz moduli. The situation for the dual shows much more involved than the case of the primal problem. |
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| Keywords: | 90C34 90C48 90C31 49J53 46A20 |
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