Selected Topics in Operations Research and Mathematical Economics

G. Hammer

ISBN 10: 3540129189 / ISBN 13: 9783540129189

Published by Springer, J.B. Metzler Apr 1984, 1984

About this Item

This item is printed on demand - Print on Demand Titel. Neuware -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].Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 496 pp. Englisch.

Seller Inventory # 9783540129189

Bibliographic Details

• Title: Selected Topics in Operations Research and Mathematical Economics
• Publisher: Springer, J.B. Metzler Apr 1984
• Publication Date: 1984
• Language: English
• ISBN 10: 3540129189
• ISBN 13: 9783540129189
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 244W x 170H x 27D millimeters 244 millimeters width by 170 millimeters height by 27 millimeters depth
• Weight: 848 grams

About this title

Synopsis

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].