Global optimization techniques for multiplicative and fractional programming problems in the image-space of objectives

• Grant number: 12/13334-1
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: January 01, 2013
• End date: June 30, 2013
• Field of knowledge: Engineering - Production Engineering - Operational Research
• Principal Investigator: Antonio Carlos Moretti
• Grantee: Alireza Mohebi Ashtiani
• Host Institution: Faculdade de Ciências Aplicadas (FCA). Universidade Estadual de Campinas (UNICAMP). Limeira , SP, Brazil

Abstract

Many practical problems in Engineering, Applied Mathematics, Physics, Science, Economics, Finance, Financial Optimization, Microeconomics, Marketing, Transportation, Strategic Planning, among others, are modeled in a very convenient way by Global Optimization problems of the NP-hard type, where the objective functions to be optimized are described by (sum of) products of two (or more) functions or (sum of) rations of functions. In such cases, the convexity of the objective function cannot be easily verified, and therefore it is reasonable to assume that there are multiple local optima. The principal objective of this research project is to introduce and develop new global optimization techniques based on global search with focus on the resolution of Generalized Multiplicative and Fractional Programming problems, two important classes of global optimization problems. The tools to be used, based on the elements of convex analysis, on the concept of level set, on the theory of duality, on the theorem of convex envelope, on the convex underestimation and on the multiobjective programming. (AU)