Minimizing the sum of a convex function and the product of two affine functions over a convex set. (English) Zbl 0817.90113

Summary: An efficient branch-and-bound algorithm for minimizing the sum of a convex function and the product of two affine functions over a convex set is proposed. The branching takes place in an interval of \(R\), the bounding is a relaxation.


90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
49J52 Nonsmooth analysis
Full Text: DOI


[1] Floudas C.A., A collection of test problems for constrained global optimization algorithms (1990) · Zbl 0718.90054
[2] DOI: 10.1287/opre.15.1.39 · Zbl 0173.21602
[3] Henderson J.M., Microeconomic theory (1971)
[4] Konno H., J. of Oper. Res. Soc. of Japan 32 pp 143– (1988)
[5] Konno H., Linear multiplicative programming (1989)
[6] Maling, K., Mueller, S.H. and Heller, W.R. On finding most optimal rectangular package plane. Proceedings of the 19th design automation conference. pp.663–670.
[7] Muu L.D., Oper. Res. Lett
[8] Muu L.D., A method for solving convex programs with an additional convex-concave constraint 112 (1989)
[9] Pardalos P.M., Quadratic programming with one negative eigenvalue is NP-hard (1990)
[10] Thach P.T., Reverse convex programs dealing with the product of two linear functions (1990)
[11] Tuy H., An efficient solution method for rank two quasiconcave minimization problem (1990)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.