On variational approach to economic equilibrium — type problem

Zdzisław Naniewicz; Magdalena Nockowska

Published: 2006-09-29

Vol. 20 (2006)

On variational approach to economic equilibrium — type problem

Zdzisław Naniewicz , Magdalena Nockowska

Abstract

The paper deals with an optimization problem in which minima of a finite collection of objective functions satisfy some unilateral constraints and are linked together by a certain subdifferential law. The governing relations are variational inequalities defined on a nonconvex feasible set. By reducing the problem to a variational inequality involving nonmonotone multivalued mapping defined over a nonnegative orthant, the existence of solutions is established under the assumption that constrained functions are positive homogeneous of degree at most one.

Keywords:

variational inequality , duality , Walrasian equilibrium

Download files

PDF

Citation rules

Naniewicz, Z., & Nockowska, M. (2006). On variational approach to economic equilibrium — type problem. Annales Mathematicae Silesianae, 20, 57–71. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14068

Similar Articles

Erwin Kasparek, Remark on invariant straight lines of some affine transformations in ℝ^n without fixed points , Annales Mathematicae Silesianae: Vol. 19 (2005)
Maciej Przybyła, Mixed stability of the d'Alembert functional equation , Annales Mathematicae Silesianae: Vol. 19 (2005)
Przemysław Tkacz, On equilibrium theorem , Annales Mathematicae Silesianae: Vol. 19 (2005)
Jaroslav Seibert, Pavel Trojovský, On divisibility of the numbers H_n(1), H_n(2) and H_n(3) , Annales Mathematicae Silesianae: Vol. 17 (2003)
Teodoro Lara, Edgar Rosales, Sandwich type results for m-convex real functions , Annales Mathematicae Silesianae: Vol. 35 No. 2 (2021)

<< < 1 2 3

You may also start an advanced similarity search for this article.

References

1. Aubin J.P., Optima and Equilibria, Springer-Verlag 1993.
2. Browder F.E., Hess P., Nonlinear mappings of monotone type in Banach spaces, J. Punct. Anal. 11 (1972), 251-294.
3. Ekeland I., Temam R., Convex Analysis and Variational Problems, North-Holland 1976.
4. Hadjisavvas N., Schaible S., From scalar to vector equilibrium problems in the quasimonotone case, J. Optim. Theory Appl. 96 (1998), 297-309.
5. Hirsh M., Smale S., On algorithms for solving f(x) = 0, Comm. Pure Appl. Math. 32 (1979), 281-312.
6. Kinderlehrer D., Stampacchia G., An Introduction to Variational Inequalities and their Applications, Academic Press 1980.
7. Lee G.M., Kim D.S., Lee B.S., Yen N.D., Vector variational inequality as a tool for studing vector optimization problems, Nonlinear Analysis 34 (1998), 745-765.
8. Luc D.T., Theory of Vector optimization, Lecture Notes in Economics and Mathematical Systems, Vol. 319, Springer-Verlag 1989.
9. Naniewicz Z., On some optimization problem related to economic equilibrium, Control and Cybernetics 31 (2002), 141-165.
10. Naniewicz Z., Panagiotopoulos P.D., Mathematical Theory of Hemivariational Inequalities and Applications, Marcel Dekker 1995.
11. Pallaschke D., Rolewicz S., Foundation of Mathematical Optimization, Kluwer Academic Publishers 1997. Google Scholar

Zdzisław Naniewicz

naniewicz@uksw.edu.pl

Affiliation:

Instytut Fizyki, Wydział Matematyczno-Przyrodniczy, Uniwersytet Kardynała Stefana Wyszyńskiego w Warszawie Poland

Magdalena Nockowska

Affiliation:

Centrum Nauczania Matematyki i Fizyki oraz Instytut Matematyki, Politechnika Łódzka Poland

Vol. 20 (2006)
Published: 2006-09-29

ISSN: 0860-2107

eISSN: 2391-4238

10.2478/amsil

Publisher

University of Silesia Press

Submit