Some heuristic approaches for solving extended geometric programming problems R. Toscano 1 , S. B. Amouri Universit´ e de Lyon Laboratoire de Tribologie et de Dynamique des Syst` emes CNRS UMR5513 ECL/ENISE 58 rue Jean Parot 42023 Saint-Etienne cedex 2 Abstract. In this paper we introduce an extension of standard geometric programming (GP) problems which we call quasi geometric programming (QGP) problems. The idea behind QGP is very simple, it means that a problem become GP when some variables are kept constants. The consideration of this particular kind of nonlinear and possibly non smooth optimization problem is motivated by the fact that many engineering problems can be formulated, or well approximated, as a QGP. However, solving a QGP remains a difficult task due to its intrinsic non-convex nature. This is why we introduce some simple approaches to easily solve this kind of non-convex problems. The interesting thing is that the proposed methods does not require the development of a customized solver and works well with any existing solver able to solve conventional geometric programs. Some considerations on the robustness issue are also presented. Various optimization problems are considered to illustrate the ability of the proposed methods for solving a QGP problem. Comparison with previously published works are also given. Keywords: Non-convex optimization, Geometric Programming, Quasi Geometric Programming, GP-solver, Robust Optimization. 1 Introduction Geometric programming (GP) has proved to be a very efficient tool for solving various kinds of engineering problems. This efficiency comes from the fact that geometric programs can be transformed to convex optimization problems for which powerful global optimization methods have been developed. As a result, globally optimal solution can be computed with great efficiency, even for problems with hundreds of variables and thousands of constraints, using recently developed interior-point algorithms. A detailed tutorial of GP and compre- hensive survey of its recent applications to various engineering problems can be found in [1]. 1 E-mail address: toscano@enise.fr, Tel.:+33 477 43 84 84; fax: +33 477 43 84 99 1