Open Access

# Finding generalized Walras-Wald equilibrium

### Abstract

The Generalized Walras-Wald Equilibrium (GE) was introduced by S. I. Zuchovitsky et al. in 1973 (see \cite{17}) as an alternative to Linear Programming (LP) approach for optimal resources allocation. There are two fundamental differences between the GE and LP approach for the best resources allocation. First, the prices for goods (products) are not fixed as it is in LP; they are functions of the production output. Second, the factors (resources) used in the production process are not fixed either; they are functions of the prices for resources. In this paper we show that under natural economic assumptions on both price and factor functions the GE exists and is unique. Finding GE is equivalent to solving a variational inequality with a strongly monotone operator. For solving the variational inequality we introduce projected pseudo-gradient method. We prove that under the same assumptions on price and factor functions the projected pseudo-gradient method converges globally with $Q$-linear rate. It allows estimating its computational complexity and finding parameters critical for the complexity bound. The method can be viewed as a natural pricing mechanism for establishing economics equilibrium.

### Article Information

 Title Finding generalized Walras-Wald equilibrium Source Methods Funct. Anal. Topology, Vol. 14 (2008), no. 3, 242-254 MathSciNet MR2458489 Copyright The Author(s) 2008 (CC BY-SA)

### Authors Information

Roman A. Polyak
George Mason University, Fairfax, VA 22030, USA

### Citation Example

Roman A. Polyak, Finding generalized Walras-Wald equilibrium, Methods Funct. Anal. Topology 14 (2008), no. 3, 242-254.

### BibTex

@article {MFAT481,
AUTHOR = {Polyak, Roman A.},
TITLE = {Finding generalized Walras-Wald equilibrium},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {14},
YEAR = {2008},
NUMBER = {3},
PAGES = {242-254},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=481},
}