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Infinite Alternative Theorems and Nonsmooth Constraint Qualification Conditions

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Abstract

In this paper, some infinite alternative theorems in locally convex vector spaces are proved and some applications of these theorems in optimization theory are addressed. Extensions of constraint qualification conditions, in the absence of differentiability using Clarke’s generalized gradient and Mordukhovich’s subdifferential, in Banach and Asplund spaces are introduced; and relationships between them are established. Some of these relations, are proved using the provided alternative theorems.

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Authors and Affiliations

  1. School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Enghelab Avenue, Tehran, Iran

    Mohammad B. Asadi & Majid Soleimani-damaneh

  2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, Iran

    Majid Soleimani-damaneh

Authors
  1. Mohammad B. Asadi
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  2. Majid Soleimani-damaneh
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Correspondence to Majid Soleimani-damaneh.

Additional information

This research was in part supported by a grant from IPM (No. 90260124).

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Asadi, M.B., Soleimani-damaneh, M. Infinite Alternative Theorems and Nonsmooth Constraint Qualification Conditions. Set-Valued Var. Anal 20, 551–566 (2012). https://doi.org/10.1007/s11228-012-0211-6

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  • DOI: https://doi.org/10.1007/s11228-012-0211-6

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