Abstract
We introduce some sufficient conditions under which a generalized linear complementarity problem (GLCP) can be solved as a pure linear complementarity problem. We also establish that the GLCP is in general a NP-Hard problem.
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Chung, S. (1989), NP-Completeness of the linear complementarity problem,Journal of Optimization Theory and Applications 60, 393–399.
Cottle, R., Pang, J., and Stone, E. (1992),The Linear Complementarity Problem, Academic Press, Inc., New York.
Cottle, R., Pang, J. and Vankateswaran, V. (1989), Sufficient matrices and the linear complementarity problem,Linear Algebra and Its Applications 114/115, 231–249.
Júdice, J. and Faustino, A. (1991), A computational analysis of LCP methods for bilinear and concave quadratic programming,Computers and Operations Research 18, 645–654.
Judice, J. and Mitra, G. (1988), Reformulation of mathematical programming programs as linear complementarity problems and investigation of their solution methods,Journal of Optimization Theory and Applications 57, 123–149.
Karp, R. (1972), Reducibility among combinatorial problems, inComplexity of Computer Computation, ed. by Miller, R. and Thatcher, J., Plenum Press, New York, pp. 85–103.
Kojima, M., Mizuno, S., and Yoshise, A. (1991), AnO(√nL) iteration potential reduction algorithm for linear complementarity problems,Mathematical Programming 50, 331–342.
Konno, H. (1976), Maximization of a convex quadratic function under linear constraints,Mathematical Programming 11, 117–127.
Pardalos, P. and Rosen, J. (1987),Constrained Global Optimization: Algorithms and Applications, Lecture Notes in Computer Science268, edited by G. Goos and J. Hartmanis, Springer Verlag, New York.
Ye, Y. (1989), A fully polynomial-time approximation algorithm for computing a stationary point of the general linear complementarity problem, The University of Iowa, Working Paper Series No. 90-10.
Ye, Y. and Pardalos, P. (1991), A class of linear complementarity problems solvable in polynomial time,Linear Algebra and Its Applications 152, 3–17.
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Support of this work has been provided by the Instituto Nacional de Investigação Cientifica de Portugal (INIC) under contract 89/EXA/5.
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Júdice, J.J., Vicente, L.N. On the solution and complexity of a generalized linear complementarity problem. J Glob Optim 4, 415–424 (1994). https://doi.org/10.1007/BF01099266
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DOI: https://doi.org/10.1007/BF01099266