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.
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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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Van Hang, N.T., Yen, N.D. On the Problem of Minimizing a Difference of Polyhedral Convex Functions Under Linear Constraints. J Optim Theory Appl 171, 617–642 (2016). https://doi.org/10.1007/s10957-015-0769-x
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DOI: https://doi.org/10.1007/s10957-015-0769-x
Keywords
- d.p. programming
- Subdifferential
- Optimality conditions
- Stationary point
- Density
- Active index set
- Extreme point