On the minimization of a quasi-concave function subject to linear constraints

doi:10.1016/0167-6377(91)90030-S

Operations Research Letters

Volume 10, Issue 3, April 1991, Pages 137-141

https://doi.org/10.1016/0167-6377(91)90030-S Get rights and content

Abstract

We give an outer approximation algorithm for minimizing a quasi-concave function subject to linear constraints, which possesses certain advantages over related algorithms. It is shown that the algorithm is easily adapted for finding all feasible vertices of a polytope.

References (5)

R. Horst et al.
On finding new vertices and redundant constraints in cutting plane algorithms for global optimization
Operations Research Letters
(1988)
W. Colmenares
Un algoritmo para la minimización de funciones cóncavas en politopos

There are more references available in the full text version of this article.

Cited by (1)

A composite branch and bound, cutting plane algorithm for concave minimization over a polyhedron
1994, Computers and Operations Research
We present an algorithm that combines branch and bound with cutting planes to globally minimize a concave function over a polyhedron. The algorithm solves a series of linear underestimating subproblems over subsets of the feasible region, yielding lower and upper bounds on the optimal objective value of the original problem. The algorithm also uses a form of the Tuy cutting plane in the subproblems of the branch and bound tree. As in cone splitting algorithms for concave minimization, we construct the cutting planes such that no restrictive nondegeneracy assumptions are required and such that the hyperplanes defining the cuts do not need to be explicitly calculated, eliminating matrix inversions. An additional advantage of our algorithm is that the cuts cause the linear underestimating functions to more accurately approximate the concave objective function, yielding tighter lower bounds. Computational results with the algorithm are reported.

View full text

On the minimization of a quasi-concave function subject to linear constraints

Abstract

Operations Research Letters

Un algoritmo para la minimización de funciones cóncavas en politopos