Global solution of optimization problems with signomial parts

Abstract

In this paper a new approach for the global solution of nonconvex MINLP (Mixed Integer NonLinear Programming) problems that contain signomial (generalized geometric) expressions is proposed and illustrated. By applying different variable transformation techniques and a discretization scheme a lower bounding convex MINLP problem can be derived. The convexified MINLP problem can be solved with standard methods. The key element in this approach is that all transformations are applied termwise. In this way all convex parts of the problem are left unaffected by the transformations. The method is illustrated by four example problems.

An Efficient Global Approach for Posynomial Geometric Programming Problems

“…According to Pörn et al (2008) and Lundell and Westerlund (2009a), we can use the exponential transformation (ET) to convexify a monomial f X by the following remark.…”

A GGP approach to solve non convex min-max predictive controller for a class of constrained MIMO systems described by state-space models

“…The GGP problems occur frequently in engineering design, chemical process industry and management (see e.g., [27,[31][32][33][34]). GGP is an optimization technique for solving a class of non convex non linear programming problems [29].…”

“…The key idea is that by applying some transformations the initial non convex problem is reduced to a Reverse Convex Programming (RCP), where the objective function and the constraint functions are convex [26]. Several works have shown that geometric programming provides a powerful tool for solving nonlinear problems and even more most of them have proven the effectiveness of the convexification strategy through benchmark functions or numerical examples in real applications (see e.g., [27][28][29][30][31][32]). However, a major limitation of the GGP that it may generate a huge amount of new constraints.…”

Optimization and evolution in metabolic pathways: Global optimization techniques in Generalized Mass Action models

“…A possible way of expediting the search for global solutions for nonlinear non-convex problems consists of exploiting the structure of the involved non-convexities. The major classes of non-convex problems studied so far include concave minimization (Hansen et al, 1992) and problems with linear fractional and bilinear terms (Quesada and Grossman, 1995), and a method for problems with signomial parts (Porn et al, 2008). Different optimization strategies have also been suggested for S-system and GMA models within BST (Chang and Sahinidis, 2005;Marin-Sanguino et al, 2007;Polisetty et al, 2008;Voit, 1992).…”