Ebook: Extremal Methods and Systems Analysis: An International Symposium on the Occasion of Professor Abraham Charnes’ Sixtieth Birthday Austin, Texas, September 13 – 15, 1977

The papers appearing in this Volume were selected from a collec­ tion of papers presented at the Internationa~ Symposium on Extrema~ Methods and Systems Ana~ysis on the Occasion of Professor A. Charnes' 60th Birthday, at the University of Texas in Austin, 13-15 September 1977. As coeditors, we have followed the normal editorial procedures of scholarly journals. We have obtained invaluable assistance from a number of colleagues who essentially performed the duties of associate editors, coordinating most of the reviews. All papers except those appearing in the Historica~ Perspectives section were refereed by at least two individuals with competency in the respective area. Because of the wide range and diversity of the topics, it would have been im­ possible for us to make a consistently rational selection of papers without the help of the associate editors and referees. We are indeed grateful to them. The breadth of extremal methods and systems analysis, suggested by the range of topics covered in these papers, is characteristic of the field and also of the scholarly work of Professor Charnes. Extre­ mal methods and systems analysis has been a pioneering and systematic approach to the development and application of new scientific theories and methods for problems of management and operations in both the pri­ vate and public sectors, spanning all major disciplines from economics to engineering.

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Content:
Front Matter....Pages I-XI
Front Matter....Pages 1-1
A Biography of Professor A. Charnes and His Scientific Work....Pages 2-9
Abraham Charnes — A Strategy for Research and a Record of Results....Pages 10-24
Front Matter....Pages 51-51
Multi-Page Format Economic Systems....Pages 52-67
The Need for Dynamic Extensions of General-Equilibrium Methods....Pages 68-84
A Few Words on Application of Optimization Methods to Economic Problems....Pages 85-95
Front Matter....Pages 97-97
Designing Investment Strategies for Fixed-Income Portfolios....Pages 98-134
Multiple Criteria Decision Making for Discrete Alternatives with Ordinal Criteria....Pages 135-152
Front Matter....Pages 153-153
Generalized Inverses of Matrices and Their Applications....Pages 154-186
Cost-Flow Networks and Generalized Inverses....Pages 187-196
The Weighted Generalized Inverse in Nonlinear Programming — Active Set Selection Using a Variable-Metric Generalization of the Simplex Algorithm....Pages 197-230
Convergence Properties of Powers of Matrices with Applications to Iterative Methods for Solving Linear Systems....Pages 231-247
Front Matter....Pages 249-249
A Network Augmenting Path Basis Algorithm for Transshipment Problems....Pages 250-274
More on the More for Less Paradox in the Distribution Model....Pages 275-303
Front Matter....Pages 305-305
The Nash Solution as a Model of Rational Bargaining....Pages 306-311
Computing the Core of a Market Game....Pages 312-334
Front Matter....Pages 335-335
Second Order Theory of Extremum Problems....Pages 336-356
An Elementary Treatment of Lagrange Multipliers....Pages 357-373
Representation of Convex Sets....Pages 374-383
On One-Row Linear Programs....Pages 384-414
Duality in Fuzzy Linear Programming....Pages 415-427
Front Matter....Pages 429-429
Fractional Programming with Zero-One Variables....Pages 430-432
Quadratic Termination of Conjugate Gradient Algorithms....Pages 433-441
Rectilinear Distance Location-Allocation Problem: A Simplex Based Algorithm....Pages 442-464
Front Matter....Pages 465-465
Recent and Past Developments in the Simplicial Approximation Approach to Solving Nonlinear Equations—A Subjective View....Pages 466-480
Global Continuation Methods for Finding all Solutions to Polynomial Systems of Equations in N Variables....Pages 481-497
Worst-Case Behavior of Local Fixed-Point Algorithms....Pages 498-504
Front Matter....Pages 505-505
Quality Control and Free Boundary Problems....Pages 506-521
The Use of Stochastic Programming for the Solution of Some Problems in Statistics and Probability....Pages 522-538
Back Matter....Pages 539-548

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Content:
Front Matter....Pages I-XI
Front Matter....Pages 1-1
A Biography of Professor A. Charnes and His Scientific Work....Pages 2-9
Abraham Charnes — A Strategy for Research and a Record of Results....Pages 10-24
Front Matter....Pages 51-51
Multi-Page Format Economic Systems....Pages 52-67
The Need for Dynamic Extensions of General-Equilibrium Methods....Pages 68-84
A Few Words on Application of Optimization Methods to Economic Problems....Pages 85-95
Front Matter....Pages 97-97
Designing Investment Strategies for Fixed-Income Portfolios....Pages 98-134
Multiple Criteria Decision Making for Discrete Alternatives with Ordinal Criteria....Pages 135-152
Front Matter....Pages 153-153
Generalized Inverses of Matrices and Their Applications....Pages 154-186
Cost-Flow Networks and Generalized Inverses....Pages 187-196
The Weighted Generalized Inverse in Nonlinear Programming — Active Set Selection Using a Variable-Metric Generalization of the Simplex Algorithm....Pages 197-230
Convergence Properties of Powers of Matrices with Applications to Iterative Methods for Solving Linear Systems....Pages 231-247
Front Matter....Pages 249-249
A Network Augmenting Path Basis Algorithm for Transshipment Problems....Pages 250-274
More on the More for Less Paradox in the Distribution Model....Pages 275-303
Front Matter....Pages 305-305
The Nash Solution as a Model of Rational Bargaining....Pages 306-311
Computing the Core of a Market Game....Pages 312-334
Front Matter....Pages 335-335
Second Order Theory of Extremum Problems....Pages 336-356
An Elementary Treatment of Lagrange Multipliers....Pages 357-373
Representation of Convex Sets....Pages 374-383
On One-Row Linear Programs....Pages 384-414
Duality in Fuzzy Linear Programming....Pages 415-427
Front Matter....Pages 429-429
Fractional Programming with Zero-One Variables....Pages 430-432
Quadratic Termination of Conjugate Gradient Algorithms....Pages 433-441
Rectilinear Distance Location-Allocation Problem: A Simplex Based Algorithm....Pages 442-464
Front Matter....Pages 465-465
Recent and Past Developments in the Simplicial Approximation Approach to Solving Nonlinear Equations—A Subjective View....Pages 466-480
Global Continuation Methods for Finding all Solutions to Polynomial Systems of Equations in N Variables....Pages 481-497
Worst-Case Behavior of Local Fixed-Point Algorithms....Pages 498-504
Front Matter....Pages 505-505
Quality Control and Free Boundary Problems....Pages 506-521
The Use of Stochastic Programming for the Solution of Some Problems in Statistics and Probability....Pages 522-538
Back Matter....Pages 539-548
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