Journal ArticleDOI
V-positivity, poverses and the economic global unicity theorems of Gale and Nikaido
Abraham Charnes,William M Raike,Joel Stutz +2 more
- Vol. 19, Iss: 3, pp 115-121
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Two new concepts are introduced here: “v-positivity” and the “poverse”, which permit us to state and prove significant generalizations of the theorems just mentioned and provide access to preliminary results concerning linear inequalities by the powerful direct techniques of linear programming theory.Abstract:
Strong theorems concerning globally unique solutions to nonlinear inequalities have been obtained byGale andNikaido via P-matrix characterizations of theJacobians of the mappings involved. We introduce two new concepts here: “v-positivity” and the “poverse”. These permit us to state and prove significant generalizations of the theorems just mentioned and, equally important, provide access to preliminary results concerning linear inequalities by the powerful direct techniques of linear programming theory.read more
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Journal ArticleDOI
On univalence and P-matrices
C.B. Garcia,W.I. Zangwill +1 more
TL;DR: In this paper, it was shown that if the Jacobian of F is a P-matrix in R, then F is univalent in R. The proof is presented in such a way as to demonstrate a suggestion of Scarf that orientation arguments may provide an alternative proof of the Gale-Nikaido theorem.
Journal ArticleDOI
The Jacobian Matrix, Global Univalence and Completely Mixed Games
T. Parthasarathy,G. Ravindran +1 more
TL;DR: This paper proves global univalence results in R4 when the Jacobian matrices are of the Leontief type and proofs make use of ideas from Gale-Nikaido and some nice game theoretic results due to Kaplansky.
Journal ArticleDOI
T. Parthasarathy’s contributions to complementarity problems: a survey
TL;DR: This expository cum survey article concerns the contributions of Professor Thiruvenkatachari Parthasarathy to complementarity problems.
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Nonconvexities in Univalence
TL;DR: Conditions under which the set need not be convex are presented, demonstrating first that the set can be diffeomorphic to a convex set and, second, that theset can have holes inside of it.
References
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Book
Management Models and Industrial Applications of Linear Programming
TL;DR: In place of a survey or evaluation of industrial studies, two broad issues which are relevant to all such applications will be discussed, including the use of linear programming models as guides to data collection and analysis and prognosis of fruitful areas of additional research, especially those which appear to have been opened by industrial applications.
Journal ArticleDOI
The Jacobian matrix and global univalence of mappings
David Gale,Hukukane Nikaido +1 more