The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Numerical Optimization Methods in Economics

  • Karl Schmedders
Reference work entry


Optimization problems are ubiquitous in economics. Many of these problems are sufficiently complex that they cannot be solved analytically. Instead economists need to resort to numerical methods. This article presents the most commonly used methods for both unconstrained and constrained optimization problems in economics; it emphasizes the solid theoretical foundation of these methods, illustrating them with examples. The presentation includes a summary of the most popular software packages for numerical optimization used in economics, and closes with a description of the rapidly developing area of mathematical programs with equilibrium constraints, an area that shows great promise for numerous economic applications.


Central path Computable general equilibrium models Computational algebraic geometry Constrained optimization Global minimum Homotopy continuation methods Interior-point methods Karush-Kuhn-Tucker conditions Kuhn–Tucker conditions Lagrange multipliers Line search methods Linear independence constraint qualification (LICQ) Linear programming Local minimum Local solution Logarithmic barrier method Mathematical programs with equilibrium constraints Metaheuristics Multidimensional optimization problems Newton’s method Newton–Raphson methods Nonlinear programming Numerical optimization methods Optimality conditions Optimization algorithms Penalty methods Polynomial functions Quadratic programs Sequential quadratic programming Simplex method for solving linear programs Simulated annealing Smale’s global Newton method Steepest descent method Taylor’s th Trust region methods Unconstrained optimization 
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I am grateful for helpful discussions with Sven Leyffer and am indebted to Ken Judd, Annette Krauss, and in particular Che-Lin Su for detailed comments on earlier drafts. I also thank the editors Larry Blume and Steven Durlauf for a careful review of my initial submission.


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© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Karl Schmedders
    • 1
  1. 1.