Linear complementarity problems and multiple objective programming

An equivalence is demonstrated between solving a linear complementarity problem with general data and finding a certain subset of the efficient points of a multiple objective programming problem. A new multiple objective programming based approach to solving linear complementarity problems is presented. Results on existence, uniqueness and computational complexity are included.

[1]  M. Kostreva Block pivot methods for solving the complementarity problem , 1978 .

[2]  E. Martins On a particular quadratic network problem , 1987 .

[3]  Roger M. Y. Ho,et al.  Goal programming and extensions , 1976 .

[4]  R. Cottle,et al.  On solving linear complementarity problems as linear programs , 1978 .

[5]  B. Eaves On Quadratic Programming , 1971 .

[6]  Mark Gershon,et al.  Techniques for multiobjective decision making in systems management , 1986 .

[7]  J. B. Rosen,et al.  Global optimization approach to the linear complementarity problem , 1988 .

[8]  M. M. Kostreva,et al.  Nonconvexity in noncooperative game theory , 1989 .

[9]  Katta G. Murty,et al.  Linear complementarity, linear and nonlinear programming , 1988 .

[10]  Lotfi A. Zadeh,et al.  Optimality and non-scalar-valued performance criteria , 1963 .

[11]  David G. Luenberger,et al.  Linear and nonlinear programming , 1984 .

[12]  L. Martein Lagrange multipliers and generalized differentiable functions in vector extremum problems , 1989 .

[13]  S. J. Chung NP-Completeness of the linear complementarity problem , 1989 .

[14]  Panos M. Pardalos,et al.  Parallel search algorithms in global optimization , 1989 .

[15]  A. M. Geoffrion Proper efficiency and the theory of vector maximization , 1968 .

[16]  Reinhard Weber,et al.  The range of the efficient frontier in multiple objective linear programming , 1984, Math. Program..

[17]  Yacov Y. Haimes,et al.  Multiobjective Decision Making: Theory and Methodology , 1983 .

[18]  H. P. Benson,et al.  Existence of efficient solutions for vector maximization problems , 1978 .

[19]  A. Charnes,et al.  Goal programming and multiple objective optimizations: Part 1 , 1977 .

[20]  B. Eaves The Linear Complementarity Problem , 1971 .

[21]  Joseph G. Ecker,et al.  Finding efficient points for linear multiple objective programs , 1975, Math. Program..

[22]  C. E. Lemke,et al.  Bimatrix Equilibrium Points and Mathematical Programming , 1965 .

[23]  C. B. García,et al.  Some classes of matrices in linear complementarity theory , 1973, Math. Program..

[24]  Richard E. Wendell,et al.  Efficiency in multiple objective optimization problems , 1977, Math. Program..

[25]  T. Gal On Efficient Sets in Vector Maximum Problems — A Brief Survey , 1986 .

[26]  D. Solow,et al.  A finite descent theory for linear programming, piecewise linear convex minimization, and the linear complementarity problem , 1985 .

[27]  Olvi L. Mangasarian,et al.  Linear complementarity problems solvable by A single linear program , 1976, Math. Program..

[28]  Michael M. Kostreva,et al.  Multiple-objective programming with polynomial objectives and constraints , 1992 .