A parametric successive underestimation method for convex multiplicative programming problems

✍ Scribed by Takahito Kuno; Hiroshi Konno

• Publisher: Springer US
• Year: 1991
• Tongue: English
• Weight: 878 KB
• Volume: 1
• Category: Article
• ISSN: 0925-5001
• DOI: 10.1007/bf00119935

✦ Synopsis

This paper addresses itself to the algorithm for minimizing the product of two nonnegative convex functions over a convex set. It is shown that the global minimum of this nonconvex problem can be obtained by solving a sequence of convex programming problems. The basic idea of this algorithm is to embed the original problem into a problem in a higher dimensional space and to apply a branch-and-bound algorithm using an underestimating function. Computational results indicate that our algorithm is efficient when the objective function is the product of a linear and a quadratic functions and the constraints are linear. An extension of our algorithm for minimizing the sum of a convex function and a product of two convex functions is also discussed.