Reiner Horst

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A generalized procedure of bisection of n–simplices is introduced, where the bisection point can be an (almost) arbitrary point at one of the longest edges. It is shown that nested sequences of simplices generated by successive generalized bisection converge to a singleton, and an exact bound of the convergence speed in terms of diameter reduction is given.(More)
An important approach in multiple criteria linear programming is the optimization of some function over the ef®cient or weakly-ecient set. This is a very dicult nonconvex optimization problem, even for the case that the function to be optimized is linear. In this article we consider the problem of maximizing a concave function over the ecient or(More)
Branch and bound approaches for nonconvex programming problems had been given in [1] and [4]. Crucial for both are the use of rectangular partitions, convex envelopes and separable nonconvex portions of the objective function and constraints. We want to propose a similar algorithm which solves a sequence of problems in each of which the objective function(More)
Several (theoretical) methods have been proposed for solving concave minimization problems; very little has been done on numerical issues. In this paper, three promising approaches (Cone-Splitting, Polyhedral Annexation and Outer Approximation) are considerably modified in order to enhance efficiency. Furthermore, a report is given on implementation, test(More)