Global Optimization of Nonlinear Sums of Ratios

✍ Scribed by Harold P. Benson

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 123 KB
• Volume: 263
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.2001.7650

✦ Synopsis

The nonlinear sum of ratios problem (P) has several important applications. However, it is also a difficult problem to solve, since it generally possesses many local optima that are not global optima. In this article we present and show the convergence of an algorithm for finding a global optimal solution to problem (P). The algorithm uses a branch and bound search procedure that globally solves problem (P) by concentrating primarily on solving an equivalent outcome space version of the problem. The algorithm can be implemented by using standard convex programming methods.  2001 Academic Press p i=1 n i x /d i x . Notice that under the assumptions given, the global minimum vm of problem (P) is attained by at least one point in X. We refer to problem (P) as the nonlinear sum of ratios problem. This problem and special cases of this problem have attracted the interest of practitioners and researchers since the 1970s.