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Books : Professional & Technical : Professional Science : Mathematics : Applied : Linear Programming
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A rigorous and comprehensive treatment of network flow theory and monotropic optimization by one of the world's most renowned applied mathematicians.
This classic textbook, first published by J. Wiley & Sons, Inc., in 1984, covers extensively the duality theory and the algorithms of linear and nonlinear network optimization optimization, and their significant extensions to monotropic programming (separable convex constrained optimization problems, including linear programs).
Monotropic programming problems are characterized by a rich interplay between combinatorial structure and convexity properties. Rockafellar develops, for the first time, algorithms and a remarkably complete duality theory for these problems.
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A linear semi-infinite program is an optimization problem with linear objective functions and linear constraints in which either the number of unknowns or the number of constraints is finite. The many direct applications of linear semi-infinite optimization (or programming) have prompted considerable and increasing research effort in recent years. The authors' aim is to communicate the main theoretical ideas and applications techniques of this fascinating area, from the perspective of convex analysis. The four sections of the book cover:
* Modelling with primal and dual problems - the primal problem, space of dual variables, the dual problem.
* Linear semi-infinite systems - existence theorems, alternative theorems, redundancy phenomena, geometrical properties of the solution set.
* Theory of linear semi-infinite programming - optimality, duality, boundedness, perturbations, well-posedness.
* Methods of linear semi-infinite programming - an overview of the main numerical methods for primal and dual problems.
Exercises and examples are provided to illustrate both theory and applications. The reader is assumed to be familiar with elementary calculus, linear algebra and general topology. An appendix on convex analysis is provided to ensure that the book is self-contained. Graduate students and researchers wishing to gain a deeper understanding of the main ideas behind the the
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Applications of optimization with Xpress-MPOverview
Optimization using Mathematical Programming makes it possible to solve many economic, commercial and industrial problems. The development of powerful and easy to use software means that this tool is now available to a large audience.This book concentrates on the modeling process, which is then applied to solve 60 real problems grouped by subject into ten chapters. Besides classical industrial problems, such as transport and scheduling, there are less well known and more recent application areas such as telecommunications, personnel management and public services.
Ten chapters, each focusing on a single application domain, contain a selection of real problems. Starting with a description of each problem, the book shows how to construct and solve a mathematical programming model using Dash Optimization's powerful Xpress-MP software . Additional material at the end of each chapter and a bibliography allow the interested reader to learn more.
Who should read this book?
Decision makers, professionals and technical personnel who need to model and solve complex optimization and decision support problems.
Students of science and business/economics.
Teachers of these subjects who are looking for material for teaching modeling and case studies in optimization.Summary
What is model
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For linear optimization models that can be formulated as linear programs with the block-angular structure, i.e. independent subproblems with coupling constraints, the Dantzig-Wolfe decomposition principle provides an elegant framework of solution algorithms as well as economic interpretation. This monograph is the complete documentation of DECOMP: a robust implementation of the Dantzig-Wolfe decomposition method in FORTRAN. The code can serve as a very convenient starting point for further investigation, both computational and economic, of parallelism in large-scale systems. It can also be used as supplemental material in a second course in linear programming, computational mathematical programming, or large-scale systems.
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In recent years, there has been intense work in linear and nonlinear programming, much of it centered on understanding and extending the ideas underlying N. Karmarkar's interior-point linear programming algorithm, which was presented in 1984. This interdisciplinary research was the subject of an AMS Summer Research Conference on Mathematical Developments Arising from Linear Programming, held at Bowdoin College in the summer of 1988, which brought together researchers in mathematics, computer science, and operations research. This volume contains the proceedings from the conference.
Among the topics covered in this book are: completely integrable dynamical systems arising in optimization problems, Riemannian geometry and interior-point linear programming methods, concepts of approximate solution of linear programs, average case analysis of the simplex method, and recent results in convex polytopes. Some of the papers extend interior-point methods to quadratic programming, the linear complementarity problem, convex programming, multi-criteria optimization, and integer programming. Other papers study the continuous trajectories underlying interior point methods. This book will be an excellent resource for those interested in the latest developments arising from Karmarkar's linear programming algorithm and in path-following methods for solving
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![The New Shepherd's Lamp Video [VHS]](http://ecx.images-amazon.com/images/I/4144sdn0PRL._SL160_.jpg)
Astronomy and celestial mechanics always initiated great breakthroughs in the development of science and mathematics. The authors of the film describe these developments starting with Ptolemy and ending with contemporary satellite-steering techniques. The explanations come via conversations, illstrations, famous scientific publications and animations. The film is of interest to everyone with an interest in mathematics and science, from school students to researchers.
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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 Karmarka's algorithm. Presentations included new algorithms, new analysis of algorithms, reports on computational experience, and some other topics related to the practice of mathematical programming.
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