Muller automaton
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 defined as a function with defined as
GPs have numerous application, such as components 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.
See also
Footnotes
43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.
References
- 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
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