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- Reiner Horst, Hoang Tuy
- 1996

- Reiner Horst, Hoang Tuy
- Applied Geometry And Discrete Mathematics
- 1990

- Reiner Horst
- Math. Comput.
- 1996

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)

- Reiner Horst, Nguyen V. Thoai
- Universität Trier, Mathematik/Informatik…
- 1994

- Reiner Horst, Thai Quynh Phong, Nguyen V. Thoai, Jakob de Vries
- J. Global Optimization
- 1991

- Reiner Horst, Nguyen V. Thoai
- European Journal of Operational Research
- 1999

An important approach in multiple criteria linear programming is the optimization of some function over the ef®cient or weakly-ecient set. This is a very dicult 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 ecient or… (More)

- Reiner Horst
- Math. Program.
- 1976

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)

- Reiner Horst, Nguyen V. Thoai
- Computing
- 1989

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)

- Hoang Tuy, Reiner Horst
- Math. Program.
- 1988

- Reiner Horst, Nguyen V. Thoai, Harold P. Benson
- Math. Program.
- 1991