Christodoulos A. Floudas - Böcker

This books presents the fundamentals of nonlinear and mixed-integer optimization, and their applications in the important area of process synthesis in chemical engineering. The reader is acquainted with the basics of convex analysis and nonlinear optimization and is introduced to the elementary concepts of mixed-integer linear nonlinear optimization. Topics that are unique include the theory and methods for mixed-integer non-linear optimization, introduction to modeling issues in process synthesis, and optimization-based approaches in the synthesis of heat recovery systems, distillation-based systems, and reactor-based systems. This book fills a gap in available textbooks since there are no other books covering either the fundamentals or applications of nonlinear and mixed-integer optimization. It is designed keeping in mind that it can be used as a graduate textbook in one or two semester courses in nonlinear and mixed-integer optimization and applications in process synthesis, as well as a reference for any engineering student or researcher concerned with continuous and discrete nonlinear optimization issues in engineering design, process synthesis, process operations, applied mathematics and operations research, industrial management, and systems engineering.

The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field.In 2000, the first edition was widely acclaimed and received high praise. J.B. Rosen crowned it “an indispensable resource” and Dingzhu Du lauded it as “the standard most important reference in this very dynamic research field”. Top authors such as Herbert Hauptman (winner of the Nobel Prize) and Leonid Khachiyan (the Ellipsoid theorist) contributed and the second edition keeps these seminal entries.The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as “Algorithms for Genomics”, “Optimization and Radiotherapy Treatment Design”, and “Crew Scheduling”.

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.

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.

Optimization problems abound in most fields of science, engineering and technology. In many of these problems it is necessary to compute the global optimum (or a good approximation) of a multivariable function. The variables that define the function to be optimized can be continuous and/or discrete and, in addition, they often have to satisfy certain constraints. Global optimization problems belong to the complexity class of NP-hard problems. Such problems are difficult to solve; traditional descent optimization algorithms based on local information are inadequate for solving them. In most cases of practical interest the number of local optima increases, on the average, exponentially with the size of the problem (number of variables). Furthermore, most of the traditional approaches fail to escape from a local optimum in order to continue the search for the global solution.Global optimization has received a lot of attention in recent years, due to the success of new algorithms for solving large classes of problems from diverse areas such as computational chemistry and biology, structural optimization, computer sciences, operations research, economics, and engineering design and control. This work contains papers presented at the conference on "State of the Art in Global Optimization: Computational Methods and Applications" held at Princeton University, April 28-30, 1995. The conference presented current research on global optimization and related applications in science and engineering. The papers included cover a wide spectrum of approaches for solving global optimization problems and applications.

Significant research activities have taken place in the areas of local and global optimization in the last two decades. Many new theoretical, computational, algorithmic, and software contributions have resulted. It has been realized that despite these numerous contributions, there does not exist a systematic forum for thorough experimental computational testing and· evaluation of the proposed optimization algorithms and their implementations. Well-designed nonconvex optimization test problems are of major impor­ tance for academic and industrial researchers interested in algorithmic and software development. It is remarkable that eventhough nonconvex models dominate all the important application areas in engineering and applied sci­ ences, there is only a limited dass of reported representative test problems. This book reflects our long term efforts in designing a benchmark database and it is motivated primarily from the need for nonconvex optimization test problems. The present collection of benchmarks indudes test problems from literature studies and a large dass of applications that arise in several branches of engineering and applied science.

This text provides a unified treatment of deterministic global optimization. It introduces theoretical and algorithmic advances that address the computation and characterization of global optima, determine valid lower and upper bounds on the global minima and maxima, and enclose all solutions of nonlinear constrained systems of equations.Among its special features, the book: introduces the fundamentals of deterministic global optimization; provides a thorough treatment of decomposition-based global optimization approaches for biconvex and bilinear problems; covers global optimization methods for generalized geometric programming problems; presents in-depth global optimization algorithms for general twice continuously differentiable nonlinear problems; provides a detailed treatment of global optimization methods for mixed-integer nonlinear problems; develops global optimization approaches for the enclosure of all solutions of nonlinear constrained systems of equations; and includes many important applications from process design, synthesis, control, and operations, phase equilibrium, design under uncertainty, parameter estimation, azeotrope prediction, structure prediction in clusters and molecules, protein folding, and peptide docking.

Optimization in Computational Chemistry and Molecular Biology: Local and Global Approaches covers recent developments in optimization techniques for addressing several computational chemistry and biology problems. A tantalizing problem that cuts across the fields of computational chemistry, biology, medicine, engineering and applied mathematics is how proteins fold. Global and local optimization provide a systematic framework of conformational searches for the prediction of three-dimensional protein structures that represent the global minimum free energy, as well as low-energy biomolecular conformations. Each contribution in the book is essentially expository in nature, but of scholarly treatment. The topics covered include advances in local and global optimization approaches for molecular dynamics and modeling, distance geometry, protein folding, molecular structure refinement, protein and drug design, and molecular and peptide docking. Audience: The book is addressed not only to researchers in mathematical programming, but to all scientists in various disciplines who use optimization methods in solving problems in computational chemistry and biology.

Global Optimization has emerged as one of the most exciting new areas of mathematical programming. Global optimization has received a wide attraction from many fields in the past few years, due to the success of new algorithms for addressing previously intractable problems from diverse areas such as computational chemistry and biology, biomedicine, structural optimization, computer sciences, operations research, economics, and engineering design and control. This book contains refereed invited papers submitted at the 4th international confer­ ence on Frontiers in Global Optimization held at Santorini, Greece during June 8-12, 2003. Santorini is one of the few sites of Greece, with wild beauty created by the explosion of a volcano which is in the middle of the gulf of the island. The mystic landscape with its numerous mult-extrema, was an inspiring location particularly for researchers working on global optimization. The three previous conferences on "Recent Advances in Global Opti­ mization", "State-of-the-Art in Global Optimization", and "Optimization in Computational Chemistry and Molecular Biology: Local and Global approaches" took place at Princeton University in 1991, 1995, and 1999, respectively. The papers in this volume focus on de­ terministic methods for global optimization, stochastic methods for global optimization, distributed computing methods in global optimization, and applications of global optimiza­ tion in several branches of applied science and engineering, computer science, computational chemistry, structural biology, and bio-informatics.

Significant research activities have taken place in the areas of local and global optimization in the last two decades. Many new theoretical, computational, algorithmic, and software contributions have resulted. It has been realized that despite these numerous contributions, there does not exist a systematic forum for thorough experimental computational testing and· evaluation of the proposed optimization algorithms and their implementations. Well-designed nonconvex optimization test problems are of major impor­ tance for academic and industrial researchers interested in algorithmic and software development. It is remarkable that eventhough nonconvex models dominate all the important application areas in engineering and applied sci­ ences, there is only a limited dass of reported representative test problems. This book reflects our long term efforts in designing a benchmark database and it is motivated primarily from the need for nonconvex optimization test problems. The present collection of benchmarks indudes test problems from literature studies and a large dass of applications that arise in several branches of engineering and applied science.

This book provides a unified and insightful treatment of deterministic global optimization. It introduces theoretical and algorithmic advances that address the computation and characterization of global optima, determine valid lower and upper bounds on the global minima and maxima, and enclose all solutions of nonlinear constrained systems of equations.Among its special features, the book: Introduces the fundamentals of deterministic global optimization; Provides a thorough treatment of decomposition-based global optimization approaches for biconvex and bilinear problems; Covers global optimization methods for generalized geometric programming problems Presents in-depth global optimization algorithms for general twice continuously differentiable nonlinear problems; Provides a detailed treatment of global optimization methods for mixed-integer nonlinear problems; Develops global optimization approaches for the enclosure of all solutions of nonlinear constrained systems of equations; Includes many important applications from process design, synthesis, control, and operations, phase equilibrium, design under uncertainty, parameter estimation, azeotrope prediction, structure prediction in clusters and molecules, protein folding, and peptide docking.Audience: This book can be used as a textbook in graduate-level courses and as a desk reference for researchers in all branches of engineering and applied science, applied mathematics, industrial engineering, operations research, computer science, economics, computational chemistry and molecular biology.

Optimization in Computational Chemistry and Molecular Biology: Local and Global Approaches covers recent developments in optimization techniques for addressing several computational chemistry and biology problems. A tantalizing problem that cuts across the fields of computational chemistry, biology, medicine, engineering and applied mathematics is how proteins fold. Global and local optimization provide a systematic framework of conformational searches for the prediction of three-dimensional protein structures that represent the global minimum free energy, as well as low-energy biomolecular conformations. Each contribution in the book is essentially expository in nature, but of scholarly treatment. The topics covered include advances in local and global optimization approaches for molecular dynamics and modeling, distance geometry, protein folding, molecular structure refinement, protein and drug design, and molecular and peptide docking. Audience: The book is addressed not only to researchers in mathematical programming, but to all scientists in various disciplines who use optimization methods in solving problems in computational chemistry and biology.

Optimization problems abound in most fields of science, engineering, and tech­ nology. In many of these problems it is necessary to compute the global optimum (or a good approximation) of a multivariable function. The variables that define the function to be optimized can be continuous and/or discrete and, in addition, many times satisfy certain constraints. Global optimization problems belong to the complexity class of NP-hard prob­ lems. Such problems are very difficult to solve. Traditional descent optimization algorithms based on local information are not adequate for solving these problems. In most cases of practical interest the number of local optima increases, on the aver­ age, exponentially with the size of the problem (number of variables). Furthermore, most of the traditional approaches fail to escape from a local optimum in order to continue the search for the global solution. Global optimization has received a lot of attention in the past ten years, due to the success of new algorithms for solving large classes of problems from diverse areas such as engineering design and control, computational chemistry and biology, structural optimization, computer science, operations research, and economics. This book contains refereed invited papers presented at the conference on "State of the Art in Global Optimization: Computational Methods and Applications" held at Princeton University, April 28-30, 1995. The conference presented current re­ search on global optimization and related applications in science and engineering. The papers included in this book cover a wide spectrum of approaches for solving global optimization problems and applications.

Global Optimization has emerged as one of the most exciting new areas of mathematical programming. Global optimization has received a wide attraction from many fields in the past few years, due to the success of new algorithms for addressing previously intractable problems from diverse areas such as computational chemistry and biology, biomedicine, structural optimization, computer sciences, operations research, economics, and engineering design and control. This book contains refereed invited papers submitted at the 4th international confer­ ence on Frontiers in Global Optimization held at Santorini, Greece during June 8-12, 2003. Santorini is one of the few sites of Greece, with wild beauty created by the explosion of a volcano which is in the middle of the gulf of the island. The mystic landscape with its numerous mult-extrema, was an inspiring location particularly for researchers working on global optimization. The three previous conferences on "Recent Advances in Global Opti­ mization", "State-of-the-Art in Global Optimization", and "Optimization in Computational Chemistry and Molecular Biology: Local and Global approaches" took place at Princeton University in 1991, 1995, and 1999, respectively. The papers in this volume focus on de­ terministic methods for global optimization, stochastic methods for global optimization, distributed computing methods in global optimization, and applications of global optimiza­ tion in several branches of applied science and engineering, computer science, computational chemistry, structural biology, and bio-informatics.

Optimization in Science and Engineering is dedicated in honor of the 60th birthday of Distinguished Professor Panos M. Pardalos. Pardalos’s past and ongoing work has made a significant impact on several theoretical and applied areas in modern optimization. As tribute to the diversity of Dr. Pardalos’s work in Optimization, this book comprises a collection of contributions from experts in various fields of this rich and diverse area of science.Topics highlight recent developments and include:Deterministic global optimizationVariational inequalities and equilibrium problemsApproximation and complexity in numerical optimizationNon-smooth optimization Statistical models and data miningApplications of optimization in medicine, energy systems, and complex network analysisThis volume will be of great interest to graduate students, researchers, and practitioners, in the fields of optimization and engineering.

Optimization in Science and Engineering is dedicated in honor of the 60th birthday of Distinguished Professor Panos M. Pardalos. Pardalos’s past and ongoing work has made a significant impact on several theoretical and applied areas in modern optimization. As tribute to the diversity of Dr. Pardalos’s work in Optimization, this book comprises a collection of contributions from experts in various fields of this rich and diverse area of science.Topics highlight recent developments and include:Deterministic global optimizationVariational inequalities and equilibrium problemsApproximation and complexity in numerical optimizationNon-smooth optimization Statistical models and data miningApplications of optimization in medicine, energy systems, and complex network analysisThis volume will be of great interest to graduate students, researchers, and practitioners, in the fields of optimization and engineering.