A new polynomial-time algorithm for linear programming
Combinatorica
Pathways to the optimal set in linear programming
on Progress in Mathematical Programming: Interior-Point and Related Methods
Existence of interior points and interior paths in nonlinear monotone complementarity problems
Mathematics of Operations Research
Market Equilibrium via a Primal-Dual-Type Algorithm
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
On the complexity of price equilibria
Journal of Computer and System Sciences - STOC 2002
A Polynomial Time Algorithm for Computing the Arrow-Debreu Market Equilibrium for Linear Utilities
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Market equilibria for homothetic, quasi-concave utilities and economies of scale in production
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
On the polynomial time computation of equilibria for certain exchange economies
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
A path to the Arrow–Debreu competitive market equilibrium
Mathematical Programming: Series A and B
The computation of approximate competitive equilibrium is PPAD-hard
Information Processing Letters
A FPTAS for Computing a Symmetric Leontief Competitive Economy Equilibrium
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
The Complexity of Models of International Trade
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
A perfect price discrimination market model with production, and a (rational) convex program for it
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
Non-separable, quasiconcave utilities are easy in a perfect price discrimination market model
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Rationality and Strongly Polynomial Solvability of Eisenberg-Gale Markets with Two Agents
SIAM Journal on Discrete Mathematics
Market equilibrium under separable, piecewise-linear, concave utilities
Journal of the ACM (JACM)
An interior-point path-following algorithm for computing a Leontief economy equilibrium
Computational Optimization and Applications
A Perfect Price Discrimination Market Model with Production, and a Rational Convex Program for It
Mathematics of Operations Research
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This paper studies the equilibrium property and algorithmic complexity of the exchange market equilibrium problem with concave piecewise linear functions, which include linear and Leontief's utility functions as special cases. We show that the Fisher model again reduces to the weighted analytic center problem, and the same linear programming complexity bound applies to computing its equilibrium. However, the story for the Arrow-Debreu model with Leontief's utility becomes quite different. We show that, for the first time, solving this class of Leontief exchange economies is equivalent to solving a linear complementarity problem whose algorithmic complexity is finite but not polynomially bounded.