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

Nguyen Thi Hang () and Nguyen Dong Yen ()
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Nguyen Thi Hang: Vietnam Academy of Science and Technology
Nguyen Dong Yen: Vietnam Academy of Science and Technology

Journal of Optimization Theory and Applications, 2016, vol. 171, issue 2, No 16, 617-642

Abstract: 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; 49J52; 90C26; 90C46 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10957-015-0769-x

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