Optimization theory had evolved initially to provide generic solutions to Introduction to Applied Optimization. Front Cover · Urmila Diwekar. Provides well-written self-contained chapters, including problem sets and exercises, making it ideal for the classroom setting; Introduces applied optimization to. Provides well-written self-contained chapters, including problem sets and exercises, making it ideal for the classroom setting; Introducesapplied optimization to.
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Introduction to applied optimization Home Introduction to applied optimization.
Introduction to applied optimization
Birge University of Chicago C. Floudas Princeton University F. Giannessi University of Pisa H. Terlaky McMaster University Y. Ye Stanford University Aims and Scope Optimization has been expanding in all directions at an astonishing rate during the last few decades. New algorithmic and theoretical techniques have been developed, the diffusion into other disciplines has proceeded at a rapid pace, and our knowledge of all aspects of the field has grown even more profound.
At the same time, one of the most striking trends in optimization is the constantly increasing emphasis on the interdisciplinary nature of the field. Optimization has been a basic tool in all areas of applied mathematics, engineering, medicine, economics and other sciences. The series Springer Optimization and Its Applications publishes undergraduate and graduate textbooks, monographs and state-of-the-art expository works that focus on algorithms for solving optimization problems and also study applications involving such problems.
Some of the topics covered include nonlinear optimization convex and nonconvexnetwork flow problems, stochastic optimization, optimal control, discrete optimization, multiobjective programming, description of software packages, approximation techniques and heuristic approaches. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden.
The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper springer. To my husband Sanjay Joag for supporting my dreams and making them a reality. And To my niece Ananya whose innocence and charm provide optimism for the future.
The Analysis of Uncertainty. Minimization of Frit Mass. Minimizing the Time Devoted to Research.
Introduction to applied optimization – PDF Free Download
The Implications of Uncertainty. Optimizing a Separation Process. The Two Ito Processes. Modern society lives not only in an environment of intense competition but is also constrained to urmilz its growth in a sustainable manner with due concern for conservation of resources.
Thus, it has become imperative to plan, design, operate, and manage resources and assets in an optimal manner. Early approaches have been to optimize individual activities in a standalone manner, however, the current trend is towards an integrated approach: The functioning of a system may be governed by multiple performance objectives.
Optimizattion of such systems will call for special strategies for handling the multiple objectives to provide solutions closer to the systems requirement. Optimization under uncertainty would become increasingly important if one is to get the best out of a system plagued applide uncertain components. These issues have thrown up a large number of challenging optimization problems which need to be resolved with a set of existing and newly evolving optimization tools.
Optimization theory had evolved initially to provide generic solutions to optimization problems xiwekar linear, nonlinear, unconstrained, and constrained domains. Although the early generation of programming problems were apolied on continuous variables, various classes of assignment and design problems required handling of both integer and continuous variables leading to mixed integer linear and nonlinear programming problems Optimlzation and MINLP. The quest to seek global optima has prompted researchers to develop new optimization approaches which do not get stuck diwe,ar a local optimum, a failing of many of the mathematical programming methods.
Genetic algorithms derived from biology and simulated annealing inspired by optimality xii Idwekar of the annealing process are two such potent methods which have emerged in recent years. The developments in computing technology have placed at the disposal of the user a wide array of optimization codes with varying degrees of rigor and sophistication. The challenges to the user are manyfold. How to set up an optimization problem?
What is the most suitable optimization method to optimiaztion How to perform sensitivity analysis? This book, appropriately titled Introduction to Applied Optimization, has addressed all the issues stated above in an elegant manner.
The book has been structured to cover all key areas of optimization namely deterministic and stochastic optimization, and single and multiobjective optimization. In keeping with the application focus of the book, the reader is provided with deep insights into key aspects of an optimization problem: Types of optimization problems that can occur and the software codes available to solve these problems are presented.
The book then moves on to treat in the next two chapters two major optimization methods, namely linear programming and nonlinear programming. Simple introductory examples are used to illustrate graphically the characteristics of the feasible region and location of optima. The simplex method used for the solution of diwekkar LP problem is described in great detail.
Lagrangian formulation tto been used to develop the relationships between primal—dual problems. The transition from the continuous to discrete optimization problem is made in Chapter 4.
The distinctive character of the solution to the discrete optimization problem is demonstrated graphically with a suitable example. Developing optimal solutions using simulated annealing and genetic algorithms are also explained in great detail.
Chapter 5 deals with strategies for optimization under uncertainty. The strategy of using the mean value urmils a random variable for optimization is shown to be suboptimal. Using probabilistic information on the uncertain variable, various measures such as value of stochastic solution VSS and expected value of perfect information EVPI are developed.
Introduction to Applied Optimization – Urmila Diwekar – Google Books
The optimization problem with recourse is analyzed. The development of chance constrained programming and L-shaped decomposition methods using probability information is shown. Multiobjective optimization is treated in the next chapter. Three methods, namely the weighting method, constraint method and goal programming method are discussed. STA-NLP framework is proposed as an alternate approach urmilq handle multiobjective optimization problems.
The book ends with a treatment of optimal control in Chapter 7. The next part deals with stochastic dynamic optimization. The book concludes with a detailed study of the dynamic optimization of batch distillation.
The thorough treatment of the stochastic distillation case should provide a revealing study for the reader interested in solving dynamic optimization problems under uncertainty. The material in the book has been carefully prepared to keep the theoretical development to a minimal level while focusing aplied the principles and implementation aspects of various algorithms.
Numerous examples have been given to lend optimizztion to the presentations.
This example is used very skillfully to demonstrate the strengths and weaknesses of various optimization methods. The book with its wide coverage of most of the well-established and emerging optimization methods will be a valuable addition to the optimization literature. The book will be a valuable guide and reference material to a wide cross-section of the user community comprising students, faculty, researchers, practitioners, designers, and planners.
In this second edition, I have updated all the chapters and additional material has been added in Chapter 3 and Chapter 7. New examples have also been added in various chapters. The solution manual and case studies for this book are available online on the Springer website with the book link http: This book would not have been possible without the constant support from my husband Dr.
Sanjay Joag, and my sisters Dr. Anjali Diwekar and Dr. Thanks are also due to the many readers around the world who sent valuable feedback. Linear and nonlinear programming problems.
Pictorial representation of the numerical optimization framework. Basic solution for Exercise 2. LP with multiple solutions. The interior point method conceptual diagram. Conversion of waste to glass. Nonlinear programming graphical representation, Exercise 3. Nonlinear programming minimum, Exercise 3. Nonlinear programming multiple minima, Exercise 3. Examples of convex and nonconvex sets.
Convex and nonconvex functions and the necessary condition. Concept of local minimum and saddle point. Constrained NLP minimization with inequalities. Constrained NLP minimization with equalities and inequalities. Constrained NLP with inequality constraint. Schematic of the Newton—Raphson method. Three cylinders in a box. Simplex tableau from Table 2. Initial tableau for Example 2. The simplex tableau, Example 2.
Initial simplex appplied, Example 2. Initial tableau for the new LP. The simplex tableau, iteration 2. The primal and dual representation for an LP. Composition for the optimal solution. Yield and sale prices of products.