Ebook: 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

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].

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Content:
Front Matter....Pages I-IX
Front Matter....Pages 1-1
A Method for Linearly Constrained Minimization Problems....Pages 3-12
On a Class of Nonconvex Optimization Problems....Pages 13-29
Lower Semicontinuity of Marginal Functions....Pages 30-41
A New Approach to Symmetric Quasiconvex Conjugacy....Pages 42-48
Generalized Convexity, Functional Hulls and Applications to Conjugate Duality in Optimization....Pages 49-79
Conjugation Operators....Pages 80-97
Global Minimization of a Difference of Two Convex Functions....Pages 98-118
Closures and Neighbourhoods Induced by Tangential Approximations....Pages 119-127
Front Matter....Pages 129-129
On the Principle of “Internal Modelling” in Linear Control Theory....Pages 131-151
On Optimal Observability of Lipschitz Systems....Pages 152-158
Front Matter....Pages 159-159
Convergence of ?-Fields and Applications to Mathematical Economics....Pages 161-174
Optimal Growth Policies for Resource-Dependent Open Economies....Pages 175-187
A Characterization of the Proportional Income Tax....Pages 188-192
Duality in the Theory of Social Choice....Pages 193-204
Nonlinear Models of Business Cycle Theory....Pages 205-222
Existence of Economic Equilibrium: New Results and Open Problems....Pages 223-242
Front Matter....Pages 243-243
Silent Duel with Accuracies Less than 1....Pages 245-251
Extensions and Modifications of the ?-Value for Cooperative Games....Pages 252-261
Stochastic Games with State Independent Transitions and Separable Rewards....Pages 262-271
Core Stability and Duality of Effectivity Functions....Pages 272-287
Front Matter....Pages 243-243
A Procedure for Computing the f-Nucleolus of a Cooperative Game....Pages 288-296
Front Matter....Pages 297-297
An O (nlogn)-Algorithm for the Minimum Cost Flow Problem in Trees....Pages 299-306
A Construction for Strongly Greedy Ordered Sets....Pages 307-314
Plane Constructions for Graphs, Networks, and Maps Measurements of Planarity....Pages 315-324
On Two Problems Related to the Traveling Salesman Problem on Halin Graphs....Pages 325-335
Front Matter....Pages 337-337
Piecewise Linear Approximation of Solution Manifolds for Nonlinear Systems of Equations....Pages 339-347
Periodic Orbits of Semiflows — Local Indices and Sections....Pages 348-360
Front Matter....Pages 361-361
Monotone Decision Rules for the Two-Armed Bandit....Pages 363-368
On the Existence of Monotone Optimal Decision Rules....Pages 369-371
Integral Representation of Functionals on Arbitrary Sets of Functions....Pages 372-381
Invariance Properties of the Banach Algebra of Darboux Integrable Functions....Pages 382-411
Construction of Locally Extremal Measure Extensions....Pages 412-420
Generalized Fox Integral Equations Solved by Functional Equations....Pages 421-429
Front Matter....Pages 431-431
An Algorithm for Linear Multiple-Choice Knapsack Problem....Pages 433-439
New Algorithms and Results of Numerical Experiments for Solution of Mathematical Programming and Optimal Control Problems....Pages 440-456
Methods of Determining Systems of Time-Table Arranging with Predetermined Area....Pages 457-464
Some Remarks on the Relation between Mathematics, Computer Science, and Medicine....Pages 465-478

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Content:
Front Matter....Pages I-IX
Front Matter....Pages 1-1
A Method for Linearly Constrained Minimization Problems....Pages 3-12
On a Class of Nonconvex Optimization Problems....Pages 13-29
Lower Semicontinuity of Marginal Functions....Pages 30-41
A New Approach to Symmetric Quasiconvex Conjugacy....Pages 42-48
Generalized Convexity, Functional Hulls and Applications to Conjugate Duality in Optimization....Pages 49-79
Conjugation Operators....Pages 80-97
Global Minimization of a Difference of Two Convex Functions....Pages 98-118
Closures and Neighbourhoods Induced by Tangential Approximations....Pages 119-127
Front Matter....Pages 129-129
On the Principle of “Internal Modelling” in Linear Control Theory....Pages 131-151
On Optimal Observability of Lipschitz Systems....Pages 152-158
Front Matter....Pages 159-159
Convergence of ?-Fields and Applications to Mathematical Economics....Pages 161-174
Optimal Growth Policies for Resource-Dependent Open Economies....Pages 175-187
A Characterization of the Proportional Income Tax....Pages 188-192
Duality in the Theory of Social Choice....Pages 193-204
Nonlinear Models of Business Cycle Theory....Pages 205-222
Existence of Economic Equilibrium: New Results and Open Problems....Pages 223-242
Front Matter....Pages 243-243
Silent Duel with Accuracies Less than 1....Pages 245-251
Extensions and Modifications of the ?-Value for Cooperative Games....Pages 252-261
Stochastic Games with State Independent Transitions and Separable Rewards....Pages 262-271
Core Stability and Duality of Effectivity Functions....Pages 272-287
Front Matter....Pages 243-243
A Procedure for Computing the f-Nucleolus of a Cooperative Game....Pages 288-296
Front Matter....Pages 297-297
An O (nlogn)-Algorithm for the Minimum Cost Flow Problem in Trees....Pages 299-306
A Construction for Strongly Greedy Ordered Sets....Pages 307-314
Plane Constructions for Graphs, Networks, and Maps Measurements of Planarity....Pages 315-324
On Two Problems Related to the Traveling Salesman Problem on Halin Graphs....Pages 325-335
Front Matter....Pages 337-337
Piecewise Linear Approximation of Solution Manifolds for Nonlinear Systems of Equations....Pages 339-347
Periodic Orbits of Semiflows — Local Indices and Sections....Pages 348-360
Front Matter....Pages 361-361
Monotone Decision Rules for the Two-Armed Bandit....Pages 363-368
On the Existence of Monotone Optimal Decision Rules....Pages 369-371
Integral Representation of Functionals on Arbitrary Sets of Functions....Pages 372-381
Invariance Properties of the Banach Algebra of Darboux Integrable Functions....Pages 382-411
Construction of Locally Extremal Measure Extensions....Pages 412-420
Generalized Fox Integral Equations Solved by Functional Equations....Pages 421-429
Front Matter....Pages 431-431
An Algorithm for Linear Multiple-Choice Knapsack Problem....Pages 433-439
New Algorithms and Results of Numerical Experiments for Solution of Mathematical Programming and Optimal Control Problems....Pages 440-456
Methods of Determining Systems of Time-Table Arranging with Predetermined Area....Pages 457-464
Some Remarks on the Relation between Mathematics, Computer Science, and Medicine....Pages 465-478
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