Basic Mathematical Programming Theory

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Basic Mathematical Programming Theory

Giorgio Giorgi,Bienvenido Jiménez,Vicente Novo
Basic Mathematical Programming Theory Book PDF

Author : Giorgio Giorgi,Bienvenido Jiménez,Vicente Novo
Publisher : Unknown
Page : 0 pages
File Size : 49,9 Mb
Release : 2023
Category : Electronic
ISBN : 3031303253

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Basic Mathematical Programming Theory by Giorgio Giorgi,Bienvenido Jiménez,Vicente Novo Pdf

This book presents a unified, progressive treatment of the basic mathematical tools of mathematical programming theory. The subject of (static) optimization, also called mathematical programming, is one of the most important and widespread branches of modern mathematics, serving as a cornerstone of such scientific subjects as economic analysis, operations research, management sciences, engineering, chemistry, physics, statistics, computer science, biology, and social sciences. This book presents a unified, progressive treatment of the basic mathematical tools of mathematical programming theory. The authors expose said tools, along with results concerning the most common mathematical programming problems formulated in a finite-dimensional setting, forming the basis for further study of the basic questions on the various algorithmic methods and the most important particular applications of mathematical programming problems. This book assumes no previous experience in optimization theory, and the treatment of the various topics is largely self-contained. Prerequisites are the basic tools of differential calculus for functions of several variables, the basic notions of topology in Rn and of linear algebra, and the basic mathematical notions and theoretical background used in analyzing optimization problems. The book is aimed at both undergraduate and postgraduate students interested in mathematical programming problems but also those professionals who use optimization methods and wish to learn the more theoretical aspects of these questions.

Mathematical Programming

S. M. Sinha
Mathematical Programming Book PDF

Author : S. M. Sinha
Publisher : Elsevier
Page : 572 pages
File Size : 41,9 Mb
Release : 2005-01-01
Category : Mathematics
ISBN : 0080535933

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Mathematical Programming by S. M. Sinha Pdf

Mathematical Programming, a branch of Operations Research, is perhaps the most efficient technique in making optimal decisions. It has a very wide application in the analysis of management problems, in business and industry, in economic studies, in military problems and in many other fields of our present day activities. In this keen competetive world, the problems are getting more and more complicated ahnd efforts are being made to deal with these challenging problems. This book presents from the origin to the recent developments in mathematical programming. The book has wide coverage and is self-contained. It is suitable both as a text and as a reference. * A wide ranging all encompasing overview of mathematical programming from its origins to recent developments * A result of over thirty years of teaching experience in this feild * A self-contained guide suitable both as a text and as a reference

Mathematical Programming

Michel Minoux
Mathematical Programming Book PDF

Author : Michel Minoux
Publisher : John Wiley & Sons
Page : 526 pages
File Size : 49,9 Mb
Release : 1986
Category : Mathematics
ISBN : UOM:39015072616876

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Mathematical Programming by Michel Minoux Pdf

This comprehensive work covers the whole field of mathematical programming, including linear programming, unconstrained and constrained nonlinear programming, nondifferentiable (or nonsmooth) optimization, integer programming, large scale systems optimization, dynamic programming, and optimization in infinite dimensions. Special emphasis is placed on unifying concepts such as point-to-set maps, saddle points and perturbations functions, duality theory and its extensions.

Basic Mathematical Programming Theory

Giorgio Giorgi,Bienvenido Jiménez,Vicente Novo
Basic Mathematical Programming Theory Book PDF

Author : Giorgio Giorgi,Bienvenido Jiménez,Vicente Novo
Publisher : Springer Nature
Page : 443 pages
File Size : 48,7 Mb
Release : 2023-07-18
Category : Business & Economics
ISBN : 9783031303241

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Basic Mathematical Programming Theory by Giorgio Giorgi,Bienvenido Jiménez,Vicente Novo Pdf

The subject of (static) optimization, also called mathematical programming, is one of the most important and widespread branches of modern mathematics, serving as a cornerstone of such scientific subjects as economic analysis, operations research, management sciences, engineering, chemistry, physics, statistics, computer science, biology, and social sciences. This book presents a unified, progressive treatment of the basic mathematical tools of mathematical programming theory. The authors expose said tools, along with results concerning the most common mathematical programming problems formulated in a finite-dimensional setting, forming the basis for further study of the basic questions on the various algorithmic methods and the most important particular applications of mathematical programming problems. This book assumes no previous experience in optimization theory, and the treatment of the various topics is largely self-contained. Prerequisites are the basic tools of differential calculus for functions of several variables, the basic notions of topology and of linear algebra, and the basic mathematical notions and theoretical background used in analyzing optimization problems. The book is aimed at both undergraduate and postgraduate students interested in mathematical programming problems but also those professionals who use optimization methods and wish to learn the more theoretical aspects of these questions.

Algorithmic Principles of Mathematical Programming

Ulrich Faigle,W. Kern,G. Still
Algorithmic Principles of Mathematical Programming Book PDF

Author : Ulrich Faigle,W. Kern,G. Still
Publisher : Springer Science & Business Media
Page : 343 pages
File Size : 45,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401598965

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Algorithmic Principles of Mathematical Programming by Ulrich Faigle,W. Kern,G. Still Pdf

Algorithmic Principles of Mathematical Programming investigates the mathematical structures and principles underlying the design of efficient algorithms for optimization problems. Recent advances in algorithmic theory have shown that the traditionally separate areas of discrete optimization, linear programming, and nonlinear optimization are closely linked. This book offers a comprehensive introduction to the whole subject and leads the reader to the frontiers of current research. The prerequisites to use the book are very elementary. All the tools from numerical linear algebra and calculus are fully reviewed and developed. Rather than attempting to be encyclopedic, the book illustrates the important basic techniques with typical problems. The focus is on efficient algorithms with respect to practical usefulness. Algorithmic complexity theory is presented with the goal of helping the reader understand the concepts without having to become a theoretical specialist. Further theory is outlined and supplemented with pointers to the relevant literature.

Theory and Application of Mathematical Programming

Gautam Mitra
Theory and Application of Mathematical Programming Book PDF

Author : Gautam Mitra
Publisher : Unknown
Page : 232 pages
File Size : 40,6 Mb
Release : 1976
Category : Mathematics
ISBN : UOM:39015015631818

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Theory and Application of Mathematical Programming by Gautam Mitra Pdf

What is mathematical programming? Equivalent linear programming problems and the simplex method; Some ancillary features of the simplex method; The revised simplex method; Computational refinements and extensions within the context of the revised simplex method; Duality properties of linear programs and post optimal analysis; Integer and mixed integer linear programs; Formulating mathematical programming models: linear programming, integer programming and nonlinear programming by extending linear programming techniques; The general mathematical programming problem: lagrange and kuhn-tucker multipliers; Convex quadratic programming: its application and its solution by the use of kuhn-tucker theory; Linear programming, quadratic programming, theory of games, and the fundamental problem: algebra and combinatorics of pivot theory for such problems.

Mathematical Programming for Power Systems Operation

Alejandro Garcés
Mathematical Programming for Power Systems Operation Book PDF

Author : Alejandro Garcés
Publisher : John Wiley & Sons
Page : 293 pages
File Size : 45,7 Mb
Release : 2021-12-01
Category : Science
ISBN : 9781119747284

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Mathematical Programming for Power Systems Operation by Alejandro Garcés Pdf

Explore the theoretical foundations and real-world power system applications of convex programming In Mathematical Programming for Power System Operation with Applications in Python, Professor Alejandro Garces delivers a comprehensive overview of power system operations models with a focus on convex optimization models and their implementation in Python. Divided into two parts, the book begins with a theoretical analysis of convex optimization models before moving on to related applications in power systems operations. The author eschews concepts of topology and functional analysis found in more mathematically oriented books in favor of a more natural approach. Using this perspective, he presents recent applications of convex optimization in power system operations problems. Mathematical Programming for Power System Operation with Applications in Python uses Python and CVXPY as tools to solve power system optimization problems and includes models that can be solved with the presented framework. The book also includes: A thorough introduction to power system operation, including economic and environmental dispatch, optimal power flow, and hosting capacity Comprehensive explorations of the mathematical background of power system operation, including quadratic forms and norms and the basic theory of optimization Practical discussions of convex functions and convex sets, including affine and linear spaces, politopes, balls, and ellipsoids In-depth examinations of convex optimization, including global optimums, and first and second order conditions Perfect for undergraduate students with some knowledge in power systems analysis, generation, or distribution, Mathematical Programming for Power System Operation with Applications in Python is also an ideal resource for graduate students and engineers practicing in the area of power system optimization.

Mathematical Programming and Game Theory for Decision Making

S. K. Neogy
Mathematical Programming and Game Theory for Decision Making Book PDF

Author : S. K. Neogy
Publisher : World Scientific
Page : 498 pages
File Size : 53,8 Mb
Release : 2008
Category : Mathematics
ISBN : 9789812813220

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Mathematical Programming and Game Theory for Decision Making by S. K. Neogy Pdf

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. Sample Chapter(s). Foreword (45 KB). Chapter 1: Mathematical Programming and its Applications in Finance (177 KB). Contents: Mathematical Programming and Its Applications in Finance (L C Thomas); Anti-Stalling Pivot Rule for Linear Programs with Totally Unimodular Coefficient Matrix (S N Kabadi & A P Punnen); A New Practically Efficient Interior Point Method for Convex Quadratic Programming (K G Murty); A General Framework for the Analysis of Sets of Constraints (R Caron & T Traynor), Tolerance-Based Algorithms for the Traveling Salesman Problem (D Ghosh et al.); On the Membership Problem of the Pedigree Polytope (T S Arthanari); Exact Algorithms for a One-Defective Vertex Colouring Problem (N Achuthan et al.); Complementarity Problem Involving a Vertical Block Matrix and Its Solution Using Neural Network Model (S K Neogy et al.); Fuzzy Twin Support Vector Machines for Pattern Classification (R Khemchandani et al.); An Overview of the Minimum Sum of Absolute Errors Regression (S C Narula & J F Wellington); Hedging Against the Market with No Short Selling (S A Clark & C Srinivasan); Mathematical Programming and Electrical Network Analysis II: Computational Linear Algebra Through Network Analysis (H Narayanan); Dynamic Optimal Control Policy in Price and Quality for High Technology Product (A K Bardhan & U Chanda); Forecasting for Supply Chain and Portfolio Management (K G Murty); Variational Analysis in Bilevel Programming (S Dempe et al.); Game Engineering (R J Aumann); Games of Connectivity (P Dubey & R Garg); A Robust Feedback Nash Equilibrium in a Climate Change Policy Game (M Hennlock); De Facto Delegation and Proposer Rules (H Imai & K Yonezaki); The Bargaining Set in Effectivity Function (D Razafimahatolotra); Dynamic Oligopoly as a Mixed Large Game OCo Toy Market (A Wiszniewska-Matyszkiel); On Some Classes of Balanced Games (R B Bapat); Market Equilibrium for Combinatorial Auctions and the Matching Core of Nonnegative TU Games (S Lahiri); Continuity, Manifolds, and Arrow''s Social Choice Problem (K Saukkonen); On a Mixture Class of Stochastic Games with Ordered Field Property (S K Neogy). Readership: Researchers, professionals and advanced students in mathematical programming, game theory, management sciences and computational mathematics.

Mathematical Programming Methods

G. Zoutendijk
Mathematical Programming Methods Book PDF

Author : G. Zoutendijk
Publisher : Unknown
Page : 524 pages
File Size : 50,9 Mb
Release : 1976
Category : Mathematics
ISBN : UCAL:B4406042

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Mathematical Programming Methods by G. Zoutendijk Pdf

Theory of linear programming; The simplex method; Numerical aspects of the simplex method; Other methods for linear programming; Special structures; Post-optimal analysis; Decomposition and partitioning methods; Integer and mixed integer linear programming; Theory of nonlinear programming; General principles of a method of feasible directions; Direction generators; Linear programming and the methods of feasible directions; Unconstrained optimization; Quadratic programming; Linearly constrained nonlinear programming; General nonlinear programming.

Fractional Programming

I.M. Stancu-Minasian
Fractional Programming Book PDF

Author : I.M. Stancu-Minasian
Publisher : Springer Science & Business Media
Page : 430 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400900356

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Fractional Programming by I.M. Stancu-Minasian Pdf

Mathematical programming has know a spectacular diversification in the last few decades. This process has happened both at the level of mathematical research and at the level of the applications generated by the solution methods that were created. To write a monograph dedicated to a certain domain of mathematical programming is, under such circumstances,especially difficult. In the present monograph we opt for the domain of fractional programming. Interest of this subject was generated by the fact that various optimization problems from engineering and economics consider the minimization of a ratio between physical and/or economical functions, for example cost/time, cost/volume,cost/profit, or other quantities that measure the efficiency of a system. For example, the productivity of industrial systems, defined as the ratio between the realized services in a system within a given period of time and the utilized resources, is used as one of the best indicators of the quality of their operation. Such problems, where the objective function appears as a ratio of functions, constitute fractional programming problem. Due to its importance in modeling various decision processes in management science, operational research, and economics, and also due to its frequent appearance in other problems that are not necessarily economical, such as information theory, numerical analysis, stochastic programming, decomposition algorithms for large linear systems, etc., the fractional programming method has received particular attention in the last three decades.

Progress in Mathematical Programming

Nimrod Megiddo
Progress in Mathematical Programming Book PDF

Author : Nimrod Megiddo
Publisher : Springer Science & Business Media
Page : 164 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461396178

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Progress in Mathematical Programming by Nimrod Megiddo Pdf

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."

Mathematical Programming

Melvyn Jeter
Mathematical Programming Book PDF

Author : Melvyn Jeter
Publisher : Routledge
Page : 360 pages
File Size : 46,8 Mb
Release : 2018-05-03
Category : Business & Economics
ISBN : 9781351433136

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Mathematical Programming by Melvyn Jeter Pdf

This book serves as an introductory text in mathematical programming and optimization for students having a mathematical background that includes one semester of linear algebra and a complete calculus sequence. It includes computational examples to aid students develop computational skills.

Mathematical Programming for Operations Researchers and Computer Scientists

Albert G. Holzman
Mathematical Programming for Operations Researchers and Computer Scientists Book PDF

Author : Albert G. Holzman
Publisher : CRC Press
Page : 393 pages
File Size : 48,6 Mb
Release : 2020-11-26
Category : Computers
ISBN : 9781000146127

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Mathematical Programming for Operations Researchers and Computer Scientists by Albert G. Holzman Pdf

This book covers the fundamentals of linear programming, extension of linear programming to discrete optimization methods, multi-objective functions, quadratic programming, geometric programming, and classical calculus methods for solving nonlinear programming problems.

Theory of Optimal Control and Mathematical Programming

Michael D. Canon,Clifton D. Cullum,Elijah Polak
Theory of Optimal Control and Mathematical Programming Book PDF

Author : Michael D. Canon,Clifton D. Cullum,Elijah Polak
Publisher : New York ; Toronto : McGraw-Hill Book Company
Page : 310 pages
File Size : 54,8 Mb
Release : 1970
Category : Control theory
ISBN : UCAL:B5008623

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Theory of Optimal Control and Mathematical Programming by Michael D. Canon,Clifton D. Cullum,Elijah Polak Pdf

"This book has three basic aims: to present a unified theory of optimization, to introduce nonlinear programming algorithms to the control engineer, and to introduce the nonlinear programming expert to optimal control. This volume can be used either as a graduate text or as a reference text." --Preface.

Interior Point Methods of Mathematical Programming

Tamás Terlaky
Interior Point Methods of Mathematical Programming Book PDF

Author : Tamás Terlaky
Publisher : Springer Science & Business Media
Page : 544 pages
File Size : 40,6 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461334491

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Interior Point Methods of Mathematical Programming by Tamás Terlaky Pdf

One has to make everything as simple as possible but, never more simple. Albert Einstein Discovery consists of seeing what every body has seen and thinking what nobody has thought. Albert S. ent_Gyorgy; The primary goal of this book is to provide an introduction to the theory of Interior Point Methods (IPMs) in Mathematical Programming. At the same time, we try to present a quick overview of the impact of extensions of IPMs on smooth nonlinear optimization and to demonstrate the potential of IPMs for solving difficult practical problems. The Simplex Method has dominated the theory and practice of mathematical pro gramming since 1947 when Dantzig discovered it. In the fifties and sixties several attempts were made to develop alternative solution methods. At that time the prin cipal base of interior point methods was also developed, for example in the work of Frisch (1955), Caroll (1961), Huard (1967), Fiacco and McCormick (1968) and Dikin (1967). In 1972 Klee and Minty made explicit that in the worst case some variants of the simplex method may require an exponential amount of work to solve Linear Programming (LP) problems. This was at the time when complexity theory became a topic of great interest. People started to classify mathematical programming prob lems as efficiently (in polynomial time) solvable and as difficult (NP-hard) problems. For a while it remained open whether LP was solvable in polynomial time or not. The break-through resolution ofthis problem was obtained by Khachijan (1989).