Let eRN be the usual vector-space of real N-uples with the usual inner product denoted by (., . ). In this paper P is a nonempty compact polyhedral set of mN, f is a real-valued function defined on (RN continuously differentiable and fP is the line- ly constrained minimization problem stated as: min (f(x) I x P) For computing stationary points of problemtj) we propose a method which attempts to operate within the linear-simplex method structure. This method then appears as a same type of method as the convex-simplex method of Zangwill [6]. It is however, different and has the advantage of being less technical with regards to the Zangwill method. It has also a simple geometrical interpretation which makes it more under standable and more open to other improvements. Also in the case where f is convex an implementable line-search is proposed which is not the case in the Zangwill method. Moreover, if f(x) = (c, x) this method will coincide with the simplex method (this is also true in the case of the convex simplex method) i if f(x) = I Ixl 12 it will be almost the same as the algorithm given by Bazaraa, Goode, Rardin [2].

**Title:**Selected Topics in Operations Research and Mathematical Economics: Proceedings of the 8th Symposium on Operations Research, Held at the University of Karlsruhe, West Germany August 22 25, 1983

**Author:**G. Hammer,Diethard Pallaschke

**ISBN:**3540129189

**Publisher:**Springer

**Genre:**

**Date Published:**1984-04-01

**Pages:**482

**Alternate description:**Amazon

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