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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 EUR 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].
List of contents
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.
