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2018•Journal of Numerical Analysis and Approximation TheoryOpen access

Linear complementarity problems solvable as linear programs

Zakia Kebbiche

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Abstract

In this paper, we present a theoretical and numerical study of linear complementary problems solvable as linear programs. We give several examples of linear complementarity problems which can be solved as linear programs using linear programming appraoches. Also, we propose two examples solved by the simplex and Karmarkar's method, while the most widely know method for solving linear complementarity problems "the complementarity pivoting algorithm due to Lemke" has failed to find a solution.

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In this paper, we present a theoretical and numerical study of linear complementary problems solvable as linear programs. We give several examples of linear complementarity problems which can be solved as linear programs using linear programming appraoches. Also, we propose two examples solved by the simplex and Karmarkar's method, while the most widely know method for solving linear complementarity problems "the complementarity pivoting algorithm due to Lemke" has failed to find a solution.

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Available abstract

In this paper, we present a theoretical and numerical study of linear complementary problems solvable as linear programs. We give several examples of linear complementarity problems which can be solved as linear programs using linear programming appraoches. Also, we propose two examples solved by the simplex and Karmarkar's method, while the most widely know method for solving linear complementarity problems "the complementarity pivoting algorithm due to Lemke" has failed to find a solution.

Key concepts: Linear complementarity problem, Linear programming, Complementarity (molecular biology), Complementarity theory, Mixed complementarity problem, Criss-cross algorithm, Simplex algorithm, Mathematical optimization

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