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Roman Polyak(rpolyakgmu.edu) Abstract: We consider Nonlinear Equilibrium (NE) for optimal allocation of limited resources. The NE is a generalization of the WalrasWald equilibrium, which is equivalent to J. Nash equilibrium in an nperson concave game. Finding NE is equivalent to solving a variational inequality (VI) with a monotone and smooth operator on $\Omega = \Re_+^n\cross\Re_+^m$. The projection on $\Omega$ is a very simple procedure, therefore our main focus is two methods for which the projection on $\Omega$ is the main operation. Both projected pseudogradient (PPG) and extra pseudogradient (EPG) methods require $O(n^2)$ operations per step. We proved convergence, established global Qlinear rate and estimated computational complexity for both PPG and EPG methods. The methods can be viewed as pricing mechanisms for establishing economic equilibrium. Keywords: Nonlinear Equilibrium, Duality, WalrasWald equilibrium, Pseudogradient, Extra pseudogradient, Linear Programming Category 1: Complementarity and Variational Inequalities Category 2: Other Topics (Game Theory ) Citation: Technical Report 12_01_2012, SEOR/Math, George Mason University, Fairfax, VA, USA Download: [PDF] Entry Submitted: 05/08/2013 Modify/Update this entry  
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