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Journal of Optimization Theory and Applications

, Volume 171, Issue 2, pp 617–642 | Cite as

On the Problem of Minimizing a Difference of Polyhedral Convex Functions Under Linear Constraints

  • Nguyen Thi Van Hang
  • Nguyen Dong YenEmail author
Article

Abstract

This paper is concerned with two d.p. (difference of polyhedral convex functions) programming models, unconstrained and linearly constrained, in a finite-dimensional setting. We obtain exact formulae for the Fréchet and Mordukhovich subdifferentials of a d.p. function. We establish optimality conditions via subdifferentials in the sense of convex analysis, of Fréchet and of Mordukhovich, and describe their relationships. Existence and computation of descent and steepest descent directions for both the models are also studied.

Keywords

d.p. programming Subdifferential Optimality conditions  Stationary point Density Active index set  Extreme point 

Mathematics Subject Classification

49J52 90C26 90C46 

Notes

Acknowledgments

The authors would like to thank the reviewer for comments and suggestions improving the present paper. They would particularly like to thank Professor Boris S. Mordukhovich for supplying them valuable references and for a great encouragement. Financial support from National Foundation for Science and Technology Development (NAFOSTED, Vietnam) under Grant 101.01-2014.37 is gratefully acknowledged.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Institute of MathematicsVietnam Academy of Science and TechnologyHanoiVietnam

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