Generalized convex multiplicative programming via quasiconcave minimization. (English) Zbl 0871.90085

Jaumard, Brigitte; Meyer, Christophe; Tuy, Hoang

J. Glob. Optim. 10, No. 3, 229-256 (1997).

Summary: We present a new method for minimizing the sum of a convex function and a product of \(k\) nonnegative convex functions over a convex set. This problem is reduced to a k-dimensional quasiconcave minimization problem which is solved by a conical branch-and-bound algorithm. Comparative computational results are provided on test problems from the literature.

MSC:

90C30

Nonlinear programming

Keywords:

generalized convex multiplicative programming; conical partition; global optimization; sum of a convex function and a product of \(k\) nonnegative convex functions; quasiconcave minimization; branch-and-bound

Software:

MINOS