Geometric programming

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A geometric program (GP) is an optimization problem of the form

Minimize subject to
where are posynomials and are monomials.

In the context of geometric programming (unlike all other disciplines), a monomial is a function defined as

where and .

GPs have numerous applications, such as component sizing in IC design[1] and parameter estimation via logistic regression in statistics. The maximum likelihood estimator in logistic regression is a GP.

Convex form

Geometric programs are not (in general) convex optimization problems, but they can be transformed to convex problems by a change of variables and a transformation of the objective and constraint functions. In particular, defining , the monomial , where . Similarly, if is the posynomial

then , where and . After the change of variables, a posynomial becomes a sum of exponentials of affine functions.


Several software packages and libraries exist to assist with formulating and solving geometric programs.

  • MOSEK is a commercial solver capable of solving geometric programs as well as other non-linear optimization problems.
  • CVXOPT is an open-source solver for convex optimization problems.
  • GPkit is a Python package for cleanly defining and manipulating geometric programming models. There are a number of example GP models written with this package here.

See also


  1. ^


  • Richard J. Duffin; Elmor L. Peterson; Clarence Zener (1967). Geometric Programming. John Wiley and Sons. p. 278. ISBN 0-471-22370-0.

External links

  • S. Boyd, S. J. Kim, L. Vandenberghe, and A. Hassibi, A Tutorial on Geometric Programming
  • S. Boyd, S. J. Kim, D. Patil, and M. Horowitz Digital Circuit Optimization via Geometric Programming
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