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Complementarity Problem and Duality Over Convex Cones

Published online by Cambridge University Press:  20 November 2018

Abraham Berman
Abraham Berman*
Affiliation:
Technion-Israel Institute of Technology, Haifa, Israel
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Abstract

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The complementarity problem is defined and studied for cases where the constraints involve convex cones, thus extending the real and complex complementarity problems. Special cases of the problem are equivalent to dual, linear or quadratic, programs over polyhedral cones.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 1 , 01 March 1974 , pp. 19 - 25
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Abrams, R. A., Nonlinear programming in complex space, Ph.D. Dissertation in Applied Mathematics, Northwestern University, August, 1969.Google Scholar
2. Abrams, R. A. and Ben-Israel, A., A duality theorem for complex quadratic programming, J. Optimization Theory Appl. 4 (1969), 244-252.Google Scholar
3. Ben-Israel, A., Linear equations and inequalities on finite dimensional, real or complex, vector spaces: a unified theory, J. Math. Anal. Appl. 27 (1969), 367-389.Google Scholar
4. Berman, A., Consistency of linear inequalities over sets. Proc. Amer. Math. Soc. 36 (1972), 13-17.Google Scholar
5. Berman, A. and Ben-Israel, A., More on linear inequalities with applications to matrix theory, J. Math. Anal. Appl. 33 (1971), 482-496.Google Scholar
6. Berman, A. and Ben-Israel, A., Linear inequalities, mathematical programming and matrix theory, Math. Prog. 1 (1971), 291-300.Google Scholar
7. Cottle, R. W., On a problem in linear inequalities, J. London Math. Soc. 43 (1968), 378-384.Google Scholar
8. Cottle, R. W., The principal pivoting method of quadratic programming, in “Mathematics of the Decision Sciences” (Dantzig, G. B. and Veinott, A. F., Jr., eds.), Part 1, pp. 144-162, American Mathematical Society, Providence, R.I., 1968.Google Scholar
9. Cottle, R. W. and Dantzig, G. B., Complementary pivot theory of mathematical programming, Linear Algebra and Appl. 1 (1968), 103-125.Google Scholar
10. Dorn, W. S., Duality in quadratic programming, Quart. Appl. Math. 18 (1960), 155-162.Google Scholar
11. Frank, M. and Wolfe, P., An algorithm for quadratic programming, Naval Res. Logist. Quart. 3 (1956), 95-110.Google Scholar
12. Hanson, M. A. and Mond, B., Quadratic programming in complex space, J. Math. Anal. Appl. 20 (1967), 507-514.Google Scholar
13. Haynsworth, E. and Hoffman, A. J., Two remarks on copositive matrices, Lin. Alg. Appl. 2 (1969), 387-392.Google Scholar
14. Ingleton, A. W., A problem in linear inequalities, Proc. London Math. Soc. 16 (1966), 519- 536.Google Scholar
15. Levinson, N., Linear programming in complex space, J. Math. Anal. Appl. 14 (1966), 44-62.Google Scholar
16. McCallum, C. J., Jr., Existence theory for the complex linear complementarity problem. Report, Bell Telephone Lab. Inc. Holdmdel, New Jersey 1971.Google Scholar
17. Motzkin, T. S., Copositive quadratic forms, National Bureau of Standards Report No. 1818 (1952), 11-12.Google Scholar