On solving difference of convex functions programs with linear complementarity constraints

Hoai An Thi (), Thi Minh Tam Nguyen () and Tao Pham Dinh ()
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Hoai An Thi: Université de Lorraine, LGIPM
Thi Minh Tam Nguyen: Posts and Telecommunications Institute of Technology
Tao Pham Dinh: National Institute for Applied Sciences

Computational Optimization and Applications, 2023, vol. 86, issue 1, No 5, 163-197

Abstract: Abstract 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.

Keywords: Mathematical program with linear complementarity constraints; Difference of convex functions programming; Difference of convex functions algorithm; Difference of convex functions constraints; Penalty function; 90C26; 90C30; 90C33; 90C90 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10589-023-00487-y

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