Introduction to Optimization

Author: Pablo Pedregal
Publisher: Springer Science & Business Media
ISBN: 9780387216805
Release Date: 2006-04-18
Genre: Mathematics

This undergraduate textbook introduces students of science and engineering to the fascinating field of optimization. It is a unique book that brings together the subfields of mathematical programming, variational calculus, and optimal control, thus giving students an overall view of all aspects of optimization in a single reference. As a primer on optimization, its main goal is to provide a succinct and accessible introduction to linear programming, nonlinear programming, numerical optimization algorithms, variational problems, dynamic programming, and optimal control. Prerequisites have been kept to a minimum, although a basic knowledge of calculus, linear algebra, and differential equations is assumed.

A First Course in Combinatorial Optimization

Author: Jon Lee
Publisher: Cambridge University Press
ISBN: 0521010128
Release Date: 2004-02-09
Genre: Business & Economics

A First Course in Combinatorial Optimization is a text for a one-semester introductory graduate-level course for students of operations research, mathematics, and computer science. It is a self-contained treatment of the subject, requiring only some mathematical maturity. Topics include: linear and integer programming, polytopes, matroids and matroid optimization, shortest paths, and network flows. Central to the exposition is the polyhedral viewpoint, which is the key principle underlying the successful integer-programming approach to combinatorial-optimization problems. Another key unifying topic is matroids. The author does not dwell on data structures and implementation details, preferring to focus on the key mathematical ideas that lead to useful models and algorithms. Problems and exercises are included throughout as well as references for further study.

Iterative Methods for Optimization

Author: C. T. Kelley
Publisher: SIAM
ISBN: 161197092X
Release Date: 1999-01-01
Genre: Iterative methods (Mathematics)

This book presents a carefully selected group of methods for unconstrained and bound constrained optimization problems and analyzes them in depth both theoretically and algorithmically. It focuses on clarity in algorithmic description and analysis rather than generality, and while it provides pointers to the literature for the most general theoretical results and robust software, the author thinks it is more important that readers have a complete understanding of special cases that convey essential ideas. A companion to Kelley's book, Iterative Methods for Linear and Nonlinear Equations (SIAM, 1995), this book contains many exercises and examples and can be used as a text, a tutorial for self-study, or a reference. Iterative Methods for Optimization does more than cover traditional gradient-based optimization: it is the first book to treat sampling methods, including the Hooke-Jeeves, implicit filtering, MDS, and Nelder-Mead schemes in a unified way, and also the first book to make connections between sampling methods and the traditional gradient-methods. Each of the main algorithms in the text is described in pseudocode, and a collection of MATLAB codes is available. Thus, readers can experiment with the algorithms in an easy way as well as implement them in other languages.

Optimization Techniques

Author: L. R. Foulds
Publisher: Springer Science & Business Media
ISBN: 9781461394587
Release Date: 2012-12-06
Genre: Science

Optimization is the process by which the optimal solution to a problem, or optimum, is produced. The word optimum has come from the Latin word optimus, meaning best. And since the beginning of his existence Man has strived for that which is best. There has been a host of contributions, from Archimedes to the present day, scattered across many disciplines. Many of the earlier ideas, although interesting from a theoretical point of view, were originally of little practical use, as they involved a daunting amount of com putational effort. Now modern computers perform calculations, whose time was once estimated in man-years, in the figurative blink of an eye. Thus it has been worthwhile to resurrect many of these earlier methods. The advent of the computer has helped bring about the unification of optimization theory into a rapidly growing branch of applied mathematics. The major objective of this book is to provide an introduction to the main optimization tech niques which are at present in use. It has been written for final year undergrad uates or first year graduates studying mathematics, engineering, business, or the physical or social sciences. The book does not assume much mathemati cal knowledge. It has an appendix containing the necessary linear algebra and basic calculus, making it virtually self-contained. This text evolved out of the experience of teaching the material to finishing undergraduates and beginning graduates.


Author: Kenneth Lange
Publisher: Springer Science & Business Media
ISBN: 9781461458388
Release Date: 2013-03-19
Genre: Mathematics

Finite-dimensional optimization problems occur throughout the mathematical sciences. The majority of these problems cannot be solved analytically. This introduction to optimization attempts to strike a balance between presentation of mathematical theory and development of numerical algorithms. Building on students’ skills in calculus and linear algebra, the text provides a rigorous exposition without undue abstraction. Its stress on statistical applications will be especially appealing to graduate students of statistics and biostatistics. The intended audience also includes students in applied mathematics, computational biology, computer science, economics, and physics who want to see rigorous mathematics combined with real applications. In this second edition the emphasis remains on finite-dimensional optimization. New material has been added on the MM algorithm, block descent and ascent, and the calculus of variations. Convex calculus is now treated in much greater depth. Advanced topics such as the Fenchel conjugate, subdifferentials, duality, feasibility, alternating projections, projected gradient methods, exact penalty methods, and Bregman iteration will equip students with the essentials for understanding modern data mining techniques in high dimensions.

Foundations of Optimization

Author: Osman Güler
Publisher: Springer Science & Business Media
ISBN: 0387684077
Release Date: 2010-08-03
Genre: Business & Economics

This book covers the fundamental principles of optimization in finite dimensions. It develops the necessary material in multivariable calculus both with coordinates and coordinate-free, so recent developments such as semidefinite programming can be dealt with.


Author: Jan Brinkhuis
Publisher: Princeton University Press
ISBN: 1400829364
Release Date: 2011-02-11
Genre: Mathematics

This self-contained textbook is an informal introduction to optimization through the use of numerous illustrations and applications. The focus is on analytically solving optimization problems with a finite number of continuous variables. In addition, the authors provide introductions to classical and modern numerical methods of optimization and to dynamic optimization. The book's overarching point is that most problems may be solved by the direct application of the theorems of Fermat, Lagrange, and Weierstrass. The authors show how the intuition for each of the theoretical results can be supported by simple geometric figures. They include numerous applications through the use of varied classical and practical problems. Even experts may find some of these applications truly surprising. A basic mathematical knowledge is sufficient to understand the topics covered in this book. More advanced readers, even experts, will be surprised to see how all main results can be grounded on the Fermat-Lagrange theorem. The book can be used for courses on continuous optimization, from introductory to advanced, for any field for which optimization is relevant.

Introduction to Applied Optimization

Author: Urmila Diwekar
Publisher: Springer Science & Business Media
ISBN: 9781475737455
Release Date: 2013-03-09
Genre: Mathematics

This text presents a multi-disciplined view of optimization, providing students and researchers with a thorough examination of algorithms, methods, and tools from diverse areas of optimization without introducing excessive theoretical detail. This second edition includes additional topics, including global optimization and a real-world case study using important concepts from each chapter. Introduction to Applied Optimization is intended for advanced undergraduate and graduate students and will benefit scientists from diverse areas, including engineers.

Practical Mathematical Optimization

Author: Jan Snyman
Publisher: Springer Science & Business Media
ISBN: 9780387243498
Release Date: 2005-12-15
Genre: Mathematics

This book presents basic optimization principles and gradient-based algorithms to a general audience, in a brief and easy-to-read form. It enables professionals to apply optimization theory to engineering, physics, chemistry, or business economics.

Numerical Mathematics

Author: Alfio Maria Quarteroni
Publisher: Springer
ISBN: 9780387227504
Release Date: 2006-04-06
Genre: Mathematics

The purpose of this book is to provide the mathematical foundations of numerical methods, to analyze their basic theoretical properties and to demonstrate their performances on examples and counterexamples. Within any specific class of problems, the most appropriate scientific computing algorithms are reviewed, their theoretical analyses are carried out and the expected results are verified using the MATLAB software environment. Each chapter contains examples, exercises and applications of the theory discussed to the solution of real-life problems. While addressed to senior undergraduates and graduates in engineering, mathematics, physics and computer sciences, this text is also valuable for researchers and users of scientific computing in a large variety of professional fields.

Applied Optimization

Author: Ross Baldick
Publisher: Cambridge University Press
ISBN: 9781107394087
Release Date: 2009-01-18
Genre: Technology & Engineering

The starting point in the formulation of any numerical problem is to take an intuitive idea about the problem in question and to translate it into precise mathematical language. This book provides step-by-step descriptions of how to formulate numerical problems and develops techniques for solving them. A number of engineering case studies motivate the development of efficient algorithms that involve, in some cases, transformation of the problem from its initial formulation into a more tractable form. Five general problem classes are considered: linear systems of equations, non-linear systems of equations, unconstrained optimization, equality-constrained optimization and inequality-constrained optimization. The book contains many worked examples and homework exercises and is suitable for students of engineering or operations research taking courses in optimization. Supplementary material including solutions, lecture slides and appendices are available online at

Mathematics of Optimization

Author: Steven J. Miller
ISBN: 1470443422
Release Date: 2017
Genre: Management science

Optimization Theory is an active area of research with numerous applications; many of the books are designed for engineering classes, and thus have an emphasis on problems from such fields. Covering much of the same material, there is less emphasis on coding and detailed applications as the intended audience is more mathematical. There are still several important problems discussed (especially scheduling problems), but there is more emphasis on theory and less on the nuts and bolts of coding. A constant theme of the text is the "why" and the "how" in the subject. Why are we able to do a calculation efficiently? How should we look at a problem? Extensive effort is made to motivate the mathematics and isolate how one can apply ideas/perspectives to a variety of problems. As many of the key algorithms in the subject require too much time or detail to analyze in a first course (such as the run-time of the Simplex Algorithm), there are numerous comparisons to simpler algorithms which students have either seen or can quickly learn (such as the Euclidean algorithm) to motivate the type of results on run-time savings

Mathematical Control Theory

Author: Eduardo D. Sontag
Publisher: Springer Science & Business Media
ISBN: 9781461205777
Release Date: 2013-11-21
Genre: Mathematics

Geared primarily to an audience consisting of mathematically advanced undergraduate or beginning graduate students, this text may additionally be used by engineering students interested in a rigorous, proof-oriented systems course that goes beyond the classical frequency-domain material and more applied courses. The minimal mathematical background required is a working knowledge of linear algebra and differential equations. The book covers what constitutes the common core of control theory and is unique in its emphasis on foundational aspects. While covering a wide range of topics written in a standard theorem/proof style, it also develops the necessary techniques from scratch. In this second edition, new chapters and sections have been added, dealing with time optimal control of linear systems, variational and numerical approaches to nonlinear control, nonlinear controllability via Lie-algebraic methods, and controllability of recurrent nets and of linear systems with bounded controls.