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Advances in Optimization and Linear Programming

Advances in Optimization and Linear Programming
Author: Ivan Stanimirović
Publisher: CRC Press
Total Pages: 119
Release: 2022-01-27
Genre: Computers
ISBN: 1000522113
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This new volume provides the information needed to understand the simplex method, the revised simplex method, dual simplex method, and more for solving linear programming problems. Following a logical order, the book first gives a mathematical model of the linear problem programming and describes the usual assumptions under which the problem is solved. It gives a brief description of classic algorithms for solving linear programming problems as well as some theoretical results. It goes on to explain the definitions and solutions of linear programming problems, outlining the simplest geometric methods and showing how they can be implemented. Practical examples are included along the way. The book concludes with a discussion of multi-criteria decision-making methods. Advances in Optimization and Linear Programming is a highly useful guide to linear programming for professors and students in optimization and linear programming.

Advances In Combinatorial Optimization: Linear Programming Formulations Of The Traveling Salesman And Other Hard Combinatorial Optimization Problems

Advances In Combinatorial Optimization: Linear Programming Formulations Of The Traveling Salesman And Other Hard Combinatorial Optimization Problems
Author: Moustapha Diaby
Publisher: World Scientific
Total Pages: 218
Release: 2016-01-28
Genre: Mathematics
ISBN: 981470489X
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Combinational optimization (CO) is a topic in applied mathematics, decision science and computer science that consists of finding the best solution from a non-exhaustive search. CO is related to disciplines such as computational complexity theory and algorithm theory, and has important applications in fields such as operations research/management science, artificial intelligence, machine learning, and software engineering.Advances in Combinatorial Optimization presents a generalized framework for formulating hard combinatorial optimization problems (COPs) as polynomial sized linear programs. Though developed based on the 'traveling salesman problem' (TSP), the framework allows for the formulating of many of the well-known NP-Complete COPs directly (without the need to reduce them to other COPs) as linear programs, and demonstrates the same for three other problems (e.g. the 'vertex coloring problem' (VCP)). This work also represents a proof of the equality of the complexity classes 'P' (polynomial time) and 'NP' (nondeterministic polynomial time), and makes a contribution to the theory and application of 'extended formulations' (EFs).On a whole, Advances in Combinatorial Optimization offers new modeling and solution perspectives which will be useful to professionals, graduate students and researchers who are either involved in routing, scheduling and sequencing decision-making in particular, or in dealing with the theory of computing in general.

Progress in Mathematical Programming

Progress in Mathematical Programming
Author: Nimrod Megiddo
Publisher: Springer Science & Business Media
Total Pages: 164
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461396174
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The starting point of this volume was a conference entitled "Progress in Mathematical Programming," held at the Asilomar Conference Center in Pacific Grove, California, March 1-4, 1987. The main topic of the conference was developments in the theory and practice of linear programming since Karmarkar's algorithm. There were thirty presentations and approximately fifty people attended. Presentations included new algorithms, new analyses of algorithms, reports on computational experience, and some other topics related to the practice of mathematical programming. Interestingly, most of the progress reported at the conference was on the theoretical side. Several new polynomial algorithms for linear program ming were presented (Barnes-Chopra-Jensen, Goldfarb-Mehrotra, Gonzaga, Kojima-Mizuno-Yoshise, Renegar, Todd, Vaidya, and Ye). Other algorithms presented were by Betke-Gritzmann, Blum, Gill-Murray-Saunders-Wright, Nazareth, Vial, and Zikan-Cottle. Efforts in the theoretical analysis of algo rithms were also reported (Anstreicher, Bayer-Lagarias, Imai, Lagarias, Megiddo-Shub, Lagarias, Smale, and Vanderbei). Computational experiences were reported by Lustig, Tomlin, Todd, Tone, Ye, and Zikan-Cottle. Of special interest, although not in the main direction discussed at the conference, was the report by Rinaldi on the practical solution of some large traveling salesman problems. At the time of the conference, it was still not clear whether the new algorithms developed since Karmarkar's algorithm would replace the simplex method in practice. Alan Hoffman presented results on conditions under which linear programming problems can be solved by greedy algorithms."

Recent Advances in Global Optimization

Recent Advances in Global Optimization
Author: Christodoulos A. Floudas
Publisher: Princeton University Press
Total Pages: 644
Release: 2014-07-14
Genre: Mathematics
ISBN: 1400862523
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This book will present the papers delivered at the first U.S. conference devoted exclusively to global optimization and will thus provide valuable insights into the significant research on the topic that has been emerging during recent years. Held at Princeton University in May 1991, the conference brought together an interdisciplinary group of the most active developers of algorithms for global optimization in order to focus the attention of the mathematical programming community on the unsolved problems and diverse applications of this field. The main subjects addressed at the conference were advances in deterministic and stochastic methods for global optimization, parallel algorithms for global optimization problems, and applications of global optimization. Although global optimization is primarily a mathematical problem, it is relevant to several other disciplines, including computer science, applied mathematics, physical chemistry, molecular biology, statistics, physics, engineering, operations research, communication theory, and economics. Global optimization problems originate from a wide variety of mathematical models of real-world systems. Some of its applications are allocation and location problems and VLSI and data-base design problems. Originally published in 1991. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Linear Programming

Linear Programming
Author: Robert J Vanderbei
Publisher: Springer Science & Business Media
Total Pages: 414
Release: 2013-07-16
Genre: Business & Economics
ISBN: 1461476305
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This Fourth Edition introduces the latest theory and applications in optimization. It emphasizes constrained optimization, beginning with a substantial treatment of linear programming and then proceeding to convex analysis, network flows, integer programming, quadratic programming, and convex optimization. Readers will discover a host of practical business applications as well as non-business applications. Topics are clearly developed with many numerical examples worked out in detail. Specific examples and concrete algorithms precede more abstract topics. With its focus on solving practical problems, the book features free C programs to implement the major algorithms covered, including the two-phase simplex method, primal-dual simplex method, path-following interior-point method, and homogeneous self-dual methods. In addition, the author provides online JAVA applets that illustrate various pivot rules and variants of the simplex method, both for linear programming and for network flows. These C programs and JAVA tools can be found on the book's website. The website also includes new online instructional tools and exercises.

Advances and Trends in Optimization with Engineering Applications

Advances and Trends in Optimization with Engineering Applications
Author: TamØs Terlaky
Publisher: SIAM
Total Pages: 696
Release: 2017-04-26
Genre: Mathematics
ISBN: 1611974682
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Optimization is of critical importance in engineering. Engineers constantly strive for the best possible solutions, the most economical use of limited resources, and the greatest efficiency. As system complexity increases, these goals mandate the use of state-of-the-art optimization techniques. In recent years, the theory and methodology of optimization have seen revolutionary improvements. Moreover, the exponential growth in computational power, along with the availability of multicore computing with virtually unlimited memory and storage capacity, has fundamentally changed what engineers can do to optimize their designs. This is a two-way process: engineers benefit from developments in optimization methodology, and challenging new classes of optimization problems arise from novel engineering applications. Advances and Trends in Optimization with Engineering Applications reviews 10 major areas of optimization and related engineering applications, providing a broad summary of state-of-the-art optimization techniques most important to engineering practice. Each part provides a clear overview of a specific area and discusses a range of real-world problems. The book provides a solid foundation for engineers and mathematical optimizers alike who want to understand the importance of optimization methods to engineering and the capabilities of these methods.

Linear and Mixed Integer Programming for Portfolio Optimization

Linear and Mixed Integer Programming for Portfolio Optimization
Author: Renata Mansini
Publisher: Springer
Total Pages: 131
Release: 2015-06-10
Genre: Business & Economics
ISBN: 3319184822
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This book presents solutions to the general problem of single period portfolio optimization. It introduces different linear models, arising from different performance measures, and the mixed integer linear models resulting from the introduction of real features. Other linear models, such as models for portfolio rebalancing and index tracking, are also covered. The book discusses computational issues and provides a theoretical framework, including the concepts of risk-averse preferences, stochastic dominance and coherent risk measures. The material is presented in a style that requires no background in finance or in portfolio optimization; some experience in linear and mixed integer models, however, is required. The book is thoroughly didactic, supplementing the concepts with comments and illustrative examples.

Theory and Algorithms for Linear Optimization

Theory and Algorithms for Linear Optimization
Author: Cornelis Roos
Publisher:
Total Pages: 520
Release: 1997-03-04
Genre: Mathematics
ISBN:
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The approach to LO in this book is new in many aspects. In particular the IPM based development of duality theory is surprisingly elegant. The algorithmic parts of the book contain a complete discussion of many algorithmic variants, including predictor-corrector methods, partial updating, higher order methods and sensitivity and parametric analysis.

Advances in Linear and Integer Programming

Advances in Linear and Integer Programming
Author: John E. Beasley
Publisher: Oxford University Press on Demand
Total Pages: 288
Release: 1996
Genre: Mathematics
ISBN: 9780198538561
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In recent years there has been an explosion of research into linear programming, as well as further steady advances in integer programming. This research has been reported in the research literature but there has been little done from the view of a "combined whole". This book aims to overcomethis. With an international authorship of contributors from acknowledged experts in their field, this book provides a clear exposition on such topics as simplex algorithms, and interior point algorithms, both from a theoretical and a computational viewpoint. Surveying recent research that iscurrently only available in journals this topical book will be of interest not only in the field of mathematics, but also in computer science and operations research as well.

Advances in Optimization and Numerical Analysis

Advances in Optimization and Numerical Analysis
Author: S. Gomez
Publisher: Springer Science & Business Media
Total Pages: 285
Release: 2013-03-09
Genre: Mathematics
ISBN: 9401583307
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In January 1992, the Sixth Workshop on Optimization and Numerical Analysis was held in the heart of the Mixteco-Zapoteca region, in the city of Oaxaca, Mexico, a beautiful and culturally rich site in ancient, colonial and modern Mexican civiliza tion. The Workshop was organized by the Numerical Analysis Department at the Institute of Research in Applied Mathematics of the National University of Mexico in collaboration with the Mathematical Sciences Department at Rice University, as were the previous ones in 1978, 1979, 1981, 1984 and 1989. As were the third, fourth, and fifth workshops, this one was supported by a grant from the Mexican National Council for Science and Technology, and the US National Science Foundation, as part of the joint Scientific and Technical Cooperation Program existing between these two countries. The participation of many of the leading figures in the field resulted in a good representation of the state of the art in Continuous Optimization, and in an over view of several topics including Numerical Methods for Diffusion-Advection PDE problems as well as some Numerical Linear Algebraic Methods to solve related pro blems. This book collects some of the papers given at this Workshop.