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Optimality Conditions Without Continuity in Multivalued Optimization Using Approximations as Generalized Derivatives

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Topics in Nonconvex Optimization

Part of the book series: Springer Optimization and Its Applications ((SOIANOIA,volume 50))

Abstract

We propose a notion of approximations as generalized derivatives for multivalued mappings and establish both necessary and sufficient conditions of orders 1 and 2 for various kinds of efficiency in multivalued vector optimization without convexity and even continuity. Compactness assumptions are also relaxed. Our theorems include several recent existing results in the literature as special cases.

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Author information

Authors and Affiliations

  1. Department of Mathematics, International University of Hochiminh City, Linh Trung, Thu Duc, Hochiminh City, Vietnam

    Phan Quoc Khanh

  2. Department of Mathematics and Statistics, University of Economics of Hochiminh City, Nguyen Dinh Chieu Street, D. 3, Hochiminh City, Vietnam

    Nguyen Dinh Tuan

Authors
  1. Phan Quoc Khanh
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  2. Nguyen Dinh Tuan
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Correspondence to Phan Quoc Khanh .

Editor information

Editors and Affiliations

  1. Faculty of Science, Dept. of Mathematics, Banaras Hindu University, Varanasi, 221005, India

    Shashi Kant Mishra

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Khanh, P.Q., Tuan, N.D. (2011). Optimality Conditions Without Continuity in Multivalued Optimization Using Approximations as Generalized Derivatives. In: Mishra, S. (eds) Topics in Nonconvex Optimization. Springer Optimization and Its Applications(), vol 50. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9640-4_3

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