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

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 condit...

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Bibliographic Details
Published inJournal of optimization theory and applications Vol. 171; no. 2; pp. 617 - 642
Main Authors Van Hang, Nguyen Thi, Yen, Nguyen Dong
Format Journal Article
LanguageEnglish
Published New York Springer US 01.11.2016
Springer Nature B.V
Subjects
Algorithms
Applications of Mathematics
Approximation
Calculus of Variations and Optimal Control; Optimization
Computation
Constraints
Convex analysis
Descent
Differential equations
Engineering
Euclidean space
Mathematical analysis
Mathematical models
Mathematical programming
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Programming
Studies
Theory of Computation
Optimality conditions
90C46
49J52
d.p. programming
Subdifferential
Extreme point
Stationary point
Active index set
90C26
Density
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-015-0769-x