Optimality and duality for nonsmooth minimax programming problems using convexifactor

I. Ahmad, Krishna Kummari, Vivek Singh, Anurag Jayswal

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


The aim of this work is to study optimality conditions for nonsmooth minimax programming problems involving locally Lipschitz functions by means of the idea of convexifactors that has been used in [J. Dutta, S. Chandra, Convexifactors, generalized convexity and vector optimization, Optimization, 53 (2004) 77-94]. Further, using the concept of optimality conditions, Mond-Weir and Wolfe type duality theory has been developed for such a minimax programming problem. The results in this paper extend the corresponding results obtained using the generalized Clarke subdifferential in the literature.

Original languageEnglish
Pages (from-to)4555-4570
Number of pages16
Issue number14
StatePublished - 2017

Bibliographical note

Funding Information:
2010 Mathematics Subject Classification. Primary 26A51; 49J35; 90C32 Keywords. Nonsmooth minimax programming, directional Dini-derivatives, convexifactor, optimality conditions, sufficiency, duality Received: 20 April 2016 ; Accepted: 15 October 2016 Communicated by Calogero Vetro The research of the fourth author is financially supported by the DST, New Delhi, India under (F. No. SR/FTP/MS-007/2011). Email addresses: drizhar@kfupm.edu.sa (I. Ahmad), krishna.maths@gmail.com (Krishna Kummari), viveksingh.25jun@gmail.com (Vivek Singh), anurag jais123@yahoo.com (Anurag Jayswal)

Publisher Copyright:
© 2017, University of Nis. All rights reserved.


  • Convexifactor
  • Directional dini-derivatives
  • Duality
  • Nonsmooth minimax programming
  • Optimality conditions
  • Sufficiency

ASJC Scopus subject areas

  • Mathematics (all)


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