Abstract
The problem considered in this paper is given by the conditions:w = q + tp + Mz, w ≥ 0,ż ≥ 0,w T ż = 0, where a dot denotes the derivative with respect to the scalar parametert ≥ 0. In this problem,q, p aren-vectors withq ≥ 0 andM is an byn P-matrix. This problem arises in a certain basic problem in the field of structural mechanics. The main result in this paper is the existence and uniqueness theorem of a solution to this problem. The existence proof is constructive providing a computational method of obtaining the solution asymptotically.
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References
R.W. Cottle, “Monotone solutions of the parametric linear complementarity problem”,Mathematical Programming 3 (1972) 210–224.
D. Gale and H. Nikaido, “The Jacobian matrix and global univalence of mappings”,Mathematische Annalen 159 (1965) 81–93.
R.L. Graves, “A principal pivoting simplex algorithm for linear and quadratic programming”,Operations Research 15 (1967) 482–494.
I. Kaneko, “Complete solutions for a class of elastic-plastic structures”, WP 77-17, Dept. of Industrial Engineering, Univ. of Wisconsin-Madison (April 1977).
I. Kaneko, “A parametric linear complementarity problem involving derivatives”, WP 77-23, Dept. of Industrial Engineering, Univ. of Wisconsin-Madison (July 1977).
G. Maier, “A matrix structural theory of piecewise-linear elasto-plasticity with interactive yield planes”,Meccanica 5 (1970) 54–66.
W. Rudin,Real and complex analysis (McGraw-Hill, N.Y., 1966).
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This research is in part supported by the National Science Foundation under Grant No. ENG77-11136.
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Kaneko, I. A parametric linear complementarity problem involving derivatives. Mathematical Programming 15, 146–154 (1978). https://doi.org/10.1007/BF01609013
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DOI: https://doi.org/10.1007/BF01609013