From linear to non-linear optimization: the missing chapter

• Published in: International journal of mathematical education in science and technology Vol. 34; no. 3; pp. 417 - 430
• Main Authors: Arsham, Hossein, Indihar Štemberger, Mojca
• Format: Journal Article
• Language: English
• Published: Taylor & Francis Group 01.01.2003
• ISSN: 0020-739X; 1464-5211
• DOI: 10.1080/0020739031000108529

Linear global optimization is the task of finding the absolute set of decision variables to optimize a given continuous function. In general, there might be several local optimal solutions and global solutions. Consequently, global optimization problems such as non-convex cases are quite difficult to solve exactly. This paper proposes an enumeration approach for solving the linearly constrained optimization problem with continuous but general objective function. This method uses a parametric but unconstrained representation of the problem in terms of the vertices (and the extreme rays) of the feasible region. The unconstrained problem is then solved by the classical unconstrained continuous optimization procedure. The aim is to propose a new introduction to optimization, the design of a general solution algorithm that is easy for the user to understand and provides useful information such as global bounding of the objective function. For illustrative and comparative purposes, the algorithm and its applications are presented in the context of numerical problems solved by other methods.