Multi-parametric disaggregation technique for global optimization of polynomial...

• Author(s): Teles, João P. ; Castro, Pedro ; Matos, Henrique A.
• Date: 2013
• Persistent ID: http://hdl.handle.net/10400.9/2444
• Origin: Repositório do LNEG
• Subject(s): Polynomial; Signomial; Optimization ; Mixed-integer linear programming; Parameterization
• Document Type: Article
• Language: English

Description

This paper discusses a power-based transformation technique that is especially useful when solving polynomial optimization problems, frequently occurring in science and engineering. The polynomial nonlinear problem is primarily transformed into a suitable reformulated problem containing new sets of discrete and continuous variables. By applying a term-wise disaggregation scheme combined with multi-parametric elements, an upper/lower bounding mixed-integer linear program can be derived for minimization/maximization problems. It can then be solved to global optimality through standard methods, with the original problem being approximated to a certain precision level, which can be as tight as desired. Furthermore, this technique can also be applied to signomial problems with rational exponents, after a few effortless algebraic transformations. Numerical examples taken from the literature are used to illustrate the effectiveness of the proposed approach.