Abstract
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 language | English |
|---|---|
| Pages (from-to) | 4555-4570 |
| Number of pages | 16 |
| Journal | Filomat |
| Volume | 31 |
| Issue number | 14 |
| DOIs | |
| State | Published - 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.
Keywords
- Convexifactor
- Directional dini-derivatives
- Duality
- Nonsmooth minimax programming
- Optimality conditions
- Sufficiency
ASJC Scopus subject areas
- Mathematics (all)