Logarithmic transformation

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Author: Hassan Ali (ChE 345 Spring 2015)

Steward: Dajun Yue, Fengqi You

Logarithmic transformation is a method used to change geometric programs into their convex forms. A geometric program, or GP, is a type of global optimization problem that concerns minimizing a subject to constraint functions so as to allow one to solve unique non-linear programming problems. All geometric programs contain functions called posynomials that are inherently non-convex. Due to this fact, solving geometric problems can be computationally intensive and finding a global optimum solution is not guaranteed. However, by creating a logarithmic transformation for a problem, one can solve for the globally optimum solution quicker and easier. A logarithmic transformation is not the only transformation which allows. One can also use an exponential transformation to obtain the same result. A logarithmic transformation can also be used on signomial programs, which are an extension of geometric programs.1,2,3



References

  1. Chiang, M. (2005). "Geometric Programming for Communication Systems", Publishers, Inc., ISBN 1-933019-09-3.
  2. Duffin, R.J. (1970). "Linearizing Geometric Programs", SIAM Review 12 (2).
  3. Ohja, A.K., Biswal, K.K. (2010). "Posynomial Geometric Programming Problems with Multiple Parameters", Journal of Computing 2 (1).