Computing Equilibria in General Equilibrium Models via Interior-point Methods

Esteban-Bravo, Mercedes

doi:10.1023/b:csem.0000021673.38534.ef

Cited by 17 publications

(12 citation statements)

References 57 publications

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“…where p is the n-dimensional optimal dual price vector of the first n equality constraints and π is the n-dimensional optimal dual price vector of the second n equality constraints in (14). We call the first set of equations the weighted centering condition, the second set of equations the complementarity condition, the third set of inequalities the dual feasibility condition, and the fourth and fifth set the primal feasibility conditions.…”

Section: An Interior-point Algorithm For Solving the Arrow-debreu Equmentioning

confidence: 99%

“…None of these are proved to be polynomial-time algorithms. Esteban-Bravo [14] recently gave another survey on linear and nonlinear optimization algorithms to compute equilibria that could be found in the computational economics literature and suggested alternative approaches, based on interior-point methods, which might be able to compute these equilibria in a practically efficient manner even for large-scale models; but no theoretical complexity analysis was presented there either.…”

Section: Introductionmentioning

confidence: 99%

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A path to the Arrow–Debreu competitive market equilibrium

2006

Math. Program.

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We present polynomial-time interior-point algorithms for solving the Fisher and Arrow-Debreu competitive market equilibrium problems with linear utilities and n players. Both of them have the arithmetic operation complexity bound of O(n 4 log(1/ )) for computing an -equilibrium solution. If the problem data are rational numbers and their bit-length is L, then the bound to generate an exact solution is O(n 4 L) which is in line with the best complexity bound for linear programming of the same dimension and size. This is a significant improvement over the previously best bound O(n 8 log(1/ )) for approximating the two problems using other methods. The key ingredient to derive these results is to show that these problems admit convex optimization formulations, efficient barrier functions and fast rounding techniques. We also present a continuous path leading to the set of the Arrow-Debreu equilibrium, similar to the central path developed for linear programming interior-point methods. This path is derived from the weighted logarithmic utility and barrier functions and the Brouwer fixed-point theorem. The defining equations are bilinear and possess some primal-dual structure for the application of the Newton-based path-following method.

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Section: An Interior-point Algorithm For Solving the Arrow-debreu Equmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A path to the Arrow–Debreu competitive market equilibrium

2006

Math. Program.

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“…Although this problem can be solved using any standard programming packages, we propose the use of the interior-point algorithm presented in Esteban-Bravo (2003). The use of interior-point methods avoids one of the weaknesses of the least-squares approach, namely, the ill-conditioning problem often observed.…”

Section: Algorithm For Deterministic Bvpmentioning

confidence: 99%

Computing continuous-time growth models with boundary conditions via wavelets

Esteban-Bravo

Vidal-Sanz

2007

Journal of Economic Dynamics and Control

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This paper presents an algorithm for approximating the solution of deterministic/stochastic continuous-time growth models based on the Euler's equation and the transversality conditions. The main issue for computing these models is to deal efficiently with the boundary conditions associated. This approach is a wavelets-collocation method derived from the finite-iterative trapezoidal approach. Illustrative examples are given. JEL classification codes: C63.

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“…This feature makes interiorpoint algorithms an attractive alternative to homotopy when considering large-scale GEI models such as the pricing of financial assets. In a recent survey, Esteban-Bravo (2004) suggests the application of interior-point methods to compute equilibria in complete markets. In this paper we fully explore this approach for solving GEI models, the complexity and scale of which demand efficient algorithms to compute equilibria.…”

Section: Introductionmentioning

confidence: 99%

An interior-point algorithm for computing equilibria in economies with incomplete asset markets

Esteban-Bravo

2008

Journal of Economic Dynamics and Control

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Computing equilibria in general equilibria models with incomplete asset (GEI) markets is technically difficult. The standard numerical methods for computing these equilibria are based on homotopy methods. Despite recent advances in computational economics, much more can be done to enlarge the catalogue of techniques for computing GEI equilibria. This paper presents an interior-point algorithm that exploits the special structure of GEI markets. We prove that the algorithm converges globally at a quadratic rate, rendering it particularly effective in solving large-scale GEI economies. To illustrate its performance, we solve relevant examples of GEI markets.

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Computing Equilibria in General Equilibrium Models via Interior-point Methods

Cited by 17 publications

References 57 publications

A path to the Arrow–Debreu competitive market equilibrium

A path to the Arrow–Debreu competitive market equilibrium

Computing continuous-time growth models with boundary conditions via wavelets

An interior-point algorithm for computing equilibria in economies with incomplete asset markets

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