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During the Spring of 1979 one of us (Zionts) was invited to visit Erasmus University in Rotterdam, The Netherlands. It was there that Zionts met another of us (Telgen) who was then in the process of completing a dissertation on redundancy in linear programming. At that time, Telgen proposed an extended visit to Buffalo, during which time he and Zionts would do an extensive study on redundancy. Redundancy, hardly an exciting or new topic, does have numerous applications. Telgen and Zionts planned the project for the Summer of 1980, and enlisted the support of all the contributors as well as the other two members of our team (Karwan and Lotfi). Lotfi was then a Ph. D. student in Industrial Engineering searching for a thesis topic. Redundancy became his topic. Karwan and Zionts served as his thesis co-chairmen, with Telgen serving as an outside reader of the thesis. We initially had hoped to complete the study during Telgen's stay in Buffalo, but that was far too optimistic. Lotfi completed his dissertation during the late Spring-early Summer of 1981. As the project took shape, we decided that we had more than enough for an article, or even several articles. Accordingly, not wanting to produce redundant papers, we decided to produce this volume --- a state-of-the-art review of methods for handling redundancy and comprehensive tests of the various methods, together with extensions and further developments of the most promising methods.
Inequalities; Equalities; Implicit equalitites; Minimal representation; Existing theory; Implicit equalities; Redundant constraints; Minimal representation; Existing methods; Results from literature; Experimental results; Nonbinding constraints; Primal-dual relations; The simplex method; The complexity of linear programming; LP-equivalent problems; The ellipsoidal method.
This edited book presents recent developments and state-of-the-art review in various areas of mathematical programming and game theory. It is a peer-reviewed research monograph under the ISI Platinum Jubilee Series on Statistical Science and Interdisciplinary Research. This volume provides a panoramic view of theory and the applications of the methods of mathematical programming to problems in statistics, finance, games and electrical networks. It also provides an important as well as timely overview of research trends and focuses on the exciting areas like support vector machines, bilevel programming, interior point method for convex quadratic programming, cooperative games, non-cooperative games and stochastic games. Researchers, professionals and advanced graduates will find the book an essential resource for current work in mathematical programming, game theory and their applications.
Abstract: "Executable codes can be extracted from constructive proofs by using realizability interpretation. However, realizability also generates redundant codes that have no significant computational meaning. This redundancy causes heavy runtime overhead, and is one of the obstacles in applying realizabilty to practical systems that realize the mathematical programming paradigm. This paper presents a method to eliminate redundancy by analyzing proof trees as pre-processing of realizability interpretation; according to the declaration given to the theorem that is proved, each node of the proof tree is marked automatically to show which part of the realizer is needed. This procedure does not always work well. This paper also gives an analysis of it and techniques to resolve critical cases. The method is studied in a simple constructive logic with primitive types, mathematical induction and its q-realizability interpretation. As an example, the extraction of a prime number checker program is given."