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selected topics in operations research and mathematical economics: proceedings of the 8th symposium on operations research, held at the university of
Diethard Pallaschke
(Ilustrado por)
·
G. Hammer
(Ilustrado por)
·
Springer
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selected topics in operations research and mathematical economics: proceedings of the 8th symposium on operations research, held at the university of - Hammer, G. ; Pallaschke, Diethard
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Reseña del libro "selected topics in operations research and mathematical economics: proceedings of the 8th symposium on operations research, held at the university of"
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].
