Global optimization problems with a quasi-concave objective function and linear constraints are studied. We point out that various other classes of global optimization problems can be expressed in this way. We present two algorithms, which can be seen as slight modifications of Benson-type algorithms for multiple objective linear programs. The modification of the MOLP algorithms results into a more efficient treatment of the studied optimization problems. This paper generalizes and improves results of Schulz and Mittal on quasi-concave problems, Shao and Ehrgott on multiplicative linear programs and L\’ohne and Wagner on minimizing the difference $f=g-h$ of two convex functions $g$, $h$ where either $g$ or $h$ is polyhedral. Numerical examples are given and the results are compared with the global optimization software BARON. A vector linear programming approach for certain global optimization problems

Advertisements