Abstract
This paper focuses on the relationship between the ‘strong’ solvability of a certain system involving a Z-function, and the strict semimonotonicity of such a function. Our main result shows that, for a system defined by a continuous, superhomogeneous Z-function, the additional condition of strict semimonotonicity is both necessary and sufficient for strong solvability.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. Berman and R.J. Plemmons,Nonnegative Square Matrices in the Mathematical Sciences (Academic Press, New York, 1979).
P. Chander, “The non-linear input-output model,”Journal of Economic Theory 30 (1983) 219–229.
M. Fiedler and V. Ptak, “On matrices with nonpositive off-diagonal elements and positive principal minors,”Czechoslovak Mathematical Journal 12 (1962) 382–400.
M. Fiedler and V. Ptak, “Some generalizations of positive definiteness and monotonicity,”Numerische Mathematik 9 (1966) 163–172.
T. Fujimoto, C. Herrero and A. Villar, “A sensitivity analysis in a nonlinear Leontief model,”Zeitschrift für Nationalökonomie 45 (1985) 67–71.
S. Karamardian, “The complementarity problem,”Mathematical Programming 2 (1972) 107–129.
S. Lahiri, “Input-output analysis with scale-dependent coefficients,”Econometrica 44 (1976) 947–962.
S. Lahiri and G. Pyatt, “On the solution of scale dependent input-output models,”Econometrica 48 (1980) 1827–1830.
J. Moré, “Classes of functions and feasibility conditions in nonlinear complementarity problems,”Mathematical Programming 6 (1974) 327–338.
J. Moré and W.C. Rheinboldt, “On P- and S-functions and related classes ofn-dimensional mappings,”Linear Algebra and Its Applications 6 (1973) 45–68.
W.C. Rheinboldt, “On M-functions and their applications to nonlinear Gauss—Seidel iterations and to network flows,”Journal of Mathematical Analysis and Applications 32 (1970) 274–307.
R.C. Ridell, “Equivalence of nonlinear complementarity problems and least element problems in Banach lattices,”Mathematics of Operations Research 6 (1981) 462–474.
I.W. Sandberg, “A nonlinear input—output model of a multisectored economy,”Econometrica 41 (1973) 1167–1182.
A. Tamir, “Minimality and complementarity properties associated with Z-functions and M-functions,”Mathematical Programming 7 (1974) 17–31.
R. Varga,Matrix Iterative Analysis (Prentice Hall, Englewood Cliffs, NJ, 1962).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Herrero, C., Silva, J.A. On the equivalence between strong solvability and strict semimonotonicity for some systems involving Z-functions. Mathematical Programming 49, 371–379 (1990). https://doi.org/10.1007/BF01588798
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01588798