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
Softcover Nachdruck of the original 1. Auflage 1984
ISBN: 978-3-540-12918-9
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 226, 482 Seiten, Paperback, Format (B × H): 170 mm x 244 mm, Gewicht: 848 g

Reihe: Lecture Notes in Economics and Mathematical Systems

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].

Zielgruppe

Research

Autoren/Hrsg.

Pallaschke, Diethard

Hammer, G.

Inhaltsverzeichnis

I: Optimization Theory.- A method for linearly constrained minimization problems.- On a class of nonconvex optimization problems.- Lower semicontinuity of marginal functions.- A new approach to symmetric quasiconvex conjugacy.- Generalized convexity, functional hulls and applications to conjugate duality in optimization.- Conjugation Operators.- Global minimization of a difference of two convex functions.- Closures and neighbourhoods induced by tangential approximations.- II: Control Theory.- On the principal of “Internal Modelling” in linear control theory.- On optimal observability of Lipschitz systems.- III: Mathematical Economics.- Convergence of ?-fields and applications to mathematical economics.- Optimal growth policies for resource-dependent open economies.- A characterization of the proportional income tax.- Duality in the theory of social choice.- Nonlinear models of business cycle theory.- Existence of economic equilibrium: new results and open problems.- IV: Game Theory.- Silent duel with accuracies less than 1.- Extensions and modifications of the ?-value for cooperative games.- Stochastic games with state independent transitions and separable rewards.- Core stability and duality of effectivity functions.- A procedure for computing the f-nucleolus of a cooperative game.- V: Graph Theory.- An O(nlogn)-algorithm for the minimum cost flow problem in trees.- A construction for strongly greedy ordered sets.- Plane constructions for graphs, networks and maps measurements of planarity.- On two problems related to the traveling salesman problem on Halin graphs.- VI: Fixed Point Theory.- Piecewise linear approximation of solution manifolds for nonlinear systems of equations.- Periodic orbits of semiflows — local indices and sections.- VII: Statistics andMeasure Theoretic Concepts.- Monotone decision rules for the two-armed bandit.- On the existence of monotone optimal decision rules.- Integral representation of functionals on arbitrary sets of functions.- Invariance properties of the Banach algebra of Darboux integrable functions.- Construction of locally extremal measure extensions.- Generalized fox integral equations solved by functional equations.- VIII: Applications.- An algorithm for linear multiple-choice Knapsack problem.- New algorithms and results of numerical experiments for solution of mathematical programming and optimal control problems.- Methods of determining systems of time-table arranging with predetermined area.- Some remarks on the relation between mathematics, computer science, and medicine.