NDLI: A FPTAS for computing a symmetric Leontief competitive economy equilibrium

Content Provider	Springer Nature Link
Author	Zhu, Zhisu Dang, Chuangyin Ye, Yinyu
Copyright Year	2010
Abstract	In this paper, we consider a linear complementarity problem (LCP) arisen from the Nash and Arrow–Debreu competitive economy equilibria where the LCP coefficient matrix is symmetric. We prove that the decision problem, to decide whether or not there exists a complementary solution, is NP-complete. Under certain conditions, an LCP solution is guaranteed to exist and we present a fully polynomial-time approximation scheme (FPTAS) for approximating a complementary solution, although the LCP solution set can be non-convex or non-connected. Our method is based on approximating a quadratic social utility optimization problem (QP) and showing that a certain KKT point of the QP problem is an LCP solution. Then, we further show that such a KKT point can be approximated with a new improved running time complexity $${{O}((\frac{n^4}{\epsilon})\log\log(\frac{1}{\epsilon}))}$$ arithmetic operation in accuracy $${\epsilon \in (0,1)}$$ . We also report preliminary computational results which show that the method is highly effective. Applications in competitive market model problems with other utility functions are also presented, including global trading and dynamic spectrum management problems.
Ending Page	129
Page Count	17
Starting Page	113
File Format	PDF
ISSN	00255610
e-ISSN	14364646
Journal	Mathematical Programming
Issue Number	1-2
Volume Number	131
Language	English
Publisher	Springer-Verlag
Publisher Date	2010-04-16
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Arrow–Debreu–Leontief General equilibrium theory Mathematical Methods in Physics Mathematics of Computing Calculus of Variations and Optimal Control; Optimization Numerical Analysis Theoretical, Mathematical and Computational Physics Linear complementarity problem Combinatorics Convex programming
Content Type	Text
Resource Type	Article
Subject	Mathematics Software

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