Kuno, Takahito A finite branch-and-bound algorithm for linear multiplicative programming. (English) Zbl 0983.90075 Comput. Optim. Appl. 20, No. 2, 119-135 (2001). Summary: On the basis of Soland’s rectangular branch and bound, we develop an algorithm for minimizing a product of \(p\) \((\geq 2)\) affine functions over a polytope. To tighten the lower bound on the value of each subproblem, we install a second-stage bounding procedure, which requires \(O(p)\) additional time in each iteration but remarkably reduces the number of branching operations. Computational results indicate that the algorithm is practical if \(p\) is less than 15, both in finding an exact optimal solution and an approximate solution. Cited in 20 Documents MSC: 90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut 90C05 Linear programming Keywords:global optimization; nonconvex optimization; affine functions over a polytope PDFBibTeX XMLCite \textit{T. Kuno}, Comput. Optim. Appl. 20, No. 2, 119--135 (2001; Zbl 0983.90075) Full Text: DOI