On solving difference of convex functions programs with linear complementarity constraints

We address a large class of Mathematical Programs with Linear Complementarity Constraints which minimizes a continuously differentiable DC function (Difference of Convex functions) on a set defined by linear constraints and linear complementarity constraints, named Difference of Convex functions pro...

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Bibliographic Details
Published in:Computational optimization and applications Vol. 86; no. 1; pp. 163 - 197
Main Authors: Le Thi, Hoai An, Nguyen, Thi Minh Tam, Dinh, Tao Pham
Format: Journal Article
Language:English
Published: New York Springer US 01.09.2023
Springer Nature B.V
Springer Verlag
Subjects:
Algorithms
Computer Science
Convex analysis
Convex and Discrete Geometry
Eigenvalues
Management Science
Mathematical programming
Mathematics
Mathematics and Statistics
Operations Research
Operations Research/Decision Theory
Optimization
Penalty function
Statistics
Mathematical program with linear complementarity constraints
Difference of convex functions algorithm
Penalty function
90C30
Difference of convex functions programming
90C33
Difference of convex functions constraints
90C90
90C26
ISSN:0926-6003, 1573-2894
Online Access:Get full text
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Summary:We address a large class of Mathematical Programs with Linear Complementarity Constraints which minimizes a continuously differentiable DC function (Difference of Convex functions) on a set defined by linear constraints and linear complementarity constraints, named Difference of Convex functions programs with Linear Complementarity Constraints. Using exact penalty techniques, we reformulate it, via four penalty functions, as standard Difference of Convex functions programs. The difference of convex functions algorithm (DCA), an efficient approach in nonconvex programming framework, is then developed to solve the resulting problems. Two particular cases are considered: quadratic problems with linear complementarity constraints and asymmetric eigenvalue complementarity problems. Numerical experiments are performed on several benchmark data, and the results show the effectiveness and the superiority of the proposed approaches comparing with some standard methods.
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-023-00487-y