A geometric program is an optimization

Optimization (mathematics)

In mathematics, computational science, or management science, mathematical optimization refers to the selection of a best element from some set of available alternatives....

 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 defined as a function with defined as


where and .

GPs have numerous application, such as components sizing in IC

Integrated circuit

An integrated circuit or monolithic integrated circuit is an electronic circuit manufactured by the patterned diffusion of trace elements into the surface of a thin substrate of semiconductor material...

 design and parameter estimation via logistic regression in statistics. The maximum likelihood

Maximum likelihood

In statistics, maximum-likelihood estimation is a method of estimating the parameters of a statistical model. When applied to a data set and given a statistical model, maximum-likelihood estimation provides estimates for the model's parameters....

 estimator in logistic regression

Logistic regression

In statistics, logistic regression is used for prediction of the probability of occurrence of an event by fitting data to a logit function logistic curve. It is a generalized linear model used for binomial 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.

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