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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Published in:	Journal of optimization theory and applications Vol. 171; no. 2; pp. 617 - 642
Main Authors:	Van Hang, Nguyen Thi, Yen, Nguyen Dong
Format:	Journal Article
Language:	English
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
ISSN:	0022-3239, 1573-2878
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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.
AbstractList	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. 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 Frechet and Mordukhovich subdifferentials of a d.p. function. We establish optimality conditions via subdifferentials in the sense of convex analysis, of Frechet and of Mordukhovich, and describe their relationships. Existence and computation of descent and steepest descent directions for both the models are also studied.
Author	Van Hang, Nguyen Thi Yen, Nguyen Dong
Author_xml	– sequence: 1 givenname: Nguyen Thi surname: Van Hang fullname: Van Hang, Nguyen Thi organization: Institute of Mathematics, Vietnam Academy of Science and Technology – sequence: 2 givenname: Nguyen Dong surname: Yen fullname: Yen, Nguyen Dong email: ndyen@math.ac.vn organization: Institute of Mathematics, Vietnam Academy of Science and Technology
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Cites_doi	10.1137/S1052623402411459 10.1080/02331930600816395 10.1515/9781400873173 10.1137/1.9781611971309 10.1080/10556780903204406 10.1023/A:1011990503369 10.1016/0377-0427(86)90075-0 10.1007/3-540-31247-1 10.1007/978-3-662-02796-7 10.1007/s10898-010-9589-6
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SubjectTerms	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
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Title	On the Problem of Minimizing a Difference of Polyhedral Convex Functions Under Linear Constraints
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