Download or read book New Simplex based Algorithms for Unconstrained Optimisation including Parallel Processing written by K. Bassiri and published by . This book was released on 1994 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "The only effective new parallel numerical algorithm for unconstrained optimisation based on the classical simplex method (which was first made usable by Nelder and Mead (1965)), is that published by Torczon (Ph. D thesis 1989, paper 1991) as the Parallel Multi-Directional Search (PMDS) algorithm. Instead of the basic step being the reflection of the single vertex which maximises the objective function, Torczon reflects all other vertices through that which minimises the objective function. PMDS therefore requires n MIMD parallel processors, where n is the dimensionality of the problem. We address the problem of employing a small fixed number, or a small fraction of n, of parallel processors to achieve more modest speed-up but with modest additional resources. Torczon's numerical results for PMDS are restricted to only two test functions namely, extended Rosenbrock and (X̲ [superscript T] X̲), each with dimesionality up to 40. However, she also found the Nelder-Mead algorithm to be widely unreliable for six test functions in that it would apparently converge to a poor approximation which could not be further improved upon. We confirmed qualitatively the latter effect which we have termed 'restricted convergence' but anticipate further detailed investigation of this curious phenomenon which we also find occurs with Torczon's method. Our attempt at an improved parallel algorithm based on the classical simplex method was successful in that one new algorithm employing only three processors would always beat the Nelder-Mead and delays the onset of restricted convergence. However, though our new algorithm is faster than PMDS at very low dimensions (where the latter is unusable), at dimensionality above about 10 it experiences difficulty in achieving an accurate result with the same two test functions, thus leaving PMDS unchallenged for speed, albeit with a heavy demand on processors/resources. Some further research, for which this report lays a foundation, is discussed in detail: modifications of PMDS have already given results for several test functions which reduce the required time by a factor of several hundred and give higher accuracy (see later reports)."

Download or read book An Introduction to Optimization written by Edwin K. P. Chong and published by John Wiley & Sons. This book was released on 2011-09-23 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise from the Second Edition "...an excellent introduction to optimization theory..." (Journal of Mathematical Psychology, 2002) "A textbook for a one-semester course on optimization theory and methods at the senior undergraduate or beginning graduate level." (SciTech Book News, Vol. 26, No. 2, June 2002) Explore the latest applications of optimization theory and methods Optimization is central to any problem involving decision making in many disciplines, such as engineering, mathematics, statistics, economics, and computer science. Now, more than ever, it is increasingly vital to have a firm grasp of the topic due to the rapid progress in computer technology, including the development and availability of user-friendly software, high-speed and parallel processors, and networks. Fully updated to reflect modern developments in the field, An Introduction to Optimization, Third Edition fills the need for an accessible, yet rigorous, introduction to optimization theory and methods. The book begins with a review of basic definitions and notations and also provides the related fundamental background of linear algebra, geometry, and calculus. With this foundation, the authors explore the essential topics of unconstrained optimization problems, linear programming problems, and nonlinear constrained optimization. An optimization perspective on global search methods is featured and includes discussions on genetic algorithms, particle swarm optimization, and the simulated annealing algorithm. In addition, the book includes an elementary introduction to artificial neural networks, convex optimization, and multi-objective optimization, all of which are of tremendous interest to students, researchers, and practitioners. Additional features of the Third Edition include: New discussions of semidefinite programming and Lagrangian algorithms A new chapter on global search methods A new chapter on multipleobjective optimization New and modified examples and exercises in each chapter as well as an updated bibliography containing new references An updated Instructor's Manual with fully worked-out solutions to the exercises Numerous diagrams and figures found throughout the text complement the written presentation of key concepts, and each chapter is followed by MATLAB exercises and drill problems that reinforce the discussed theory and algorithms. With innovative coverage and a straightforward approach, An Introduction to Optimization, Third Edition is an excellent book for courses in optimization theory and methods at the upper-undergraduate and graduate levels. It also serves as a useful, self-contained reference for researchers and professionals in a wide array of fields.

Download or read book High Performance Algorithms and Software in Nonlinear Optimization written by Renato de Leone and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a selection of papers presented at the conference on High Performance Software for Nonlinear Optimization (HPSN097) which was held in Ischia, Italy, in June 1997. The rapid progress of computer technologies, including new parallel architec tures, has stimulated a large amount of research devoted to building software environments and defining algorithms able to fully exploit this new computa tional power. In some sense, numerical analysis has to conform itself to the new tools. The impact of parallel computing in nonlinear optimization, which had a slow start at the beginning, seems now to increase at a fast rate, and it is reasonable to expect an even greater acceleration in the future. As with the first HPSNO conference, the goal of the HPSN097 conference was to supply a broad overview of the more recent developments and trends in nonlinear optimization, emphasizing the algorithmic and high performance software aspects. Bringing together new computational methodologies with theoretical ad vances and new computer technologies is an exciting challenge that involves all scientists willing to develop high performance numerical software. This book contains several important contributions from different and com plementary standpoints. Obviously, the articles in the book do not cover all the areas of the conference topic or all the most recent developments, because of the large number of new theoretical and computational ideas of the last few years.

Download or read book Algorithms for Continuous Optimization written by E. Spedicato and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: The NATO Advanced Study Institute on "Algorithms for continuous optimiza tion: the state of the art" was held September 5-18, 1993, at II Ciocco, Barga, Italy. It was attended by 75 students (among them many well known specialists in optimiza tion) from the following countries: Belgium, Brasil, Canada, China, Czech Republic, France, Germany, Greece, Hungary, Italy, Poland, Portugal, Rumania, Spain, Turkey, UK, USA, Venezuela. The lectures were given by 17 well known specialists in the field, from Brasil, China, Germany, Italy, Portugal, Russia, Sweden, UK, USA. Solving continuous optimization problems is a fundamental task in computational mathematics for applications in areas of engineering, economics, chemistry, biology and so on. Most real problems are nonlinear and can be of quite large size. Devel oping efficient algorithms for continuous optimization has been an important field of research in the last 30 years, with much additional impetus provided in the last decade by the availability of very fast and parallel computers. Techniques, like the simplex method, that were already considered fully developed thirty years ago have been thoroughly revised and enormously improved. The aim of this ASI was to present the state of the art in this field. While not all important aspects could be covered in the fifty hours of lectures (for instance multiob jective optimization had to be skipped), we believe that most important topics were presented, many of them by scientists who greatly contributed to their development.

Download or read book HERMIS 94 written by and published by . This book was released on 1994 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Topics in Parallel Computing in Mathematical Programming written by Panos M. Pardalos and published by . This book was released on 1992 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Multi directional Parallel Algorithms for Unconstrained Optimization written by National University of Singapore. Dept. of Information Systems and Computer Science and published by . This book was released on 1993 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "Parallel algorithms for solving unconstrained nonlinear optimization problems are presented. These algorithms are based on the quasi-Newton methods. At each step of the algorithms, several search directions are generated in parallel using various quasi-Newton updates. Our numerical results show significant improvement in the number of iterations and function evaluations required by the parallel algorithms over those required by the serial quasi-Newton updates such as the SR1 method or the BFGS method for many of the test problems."

Download or read book Functional Informatics in Drug Discovery written by Sergey Ilyin and published by CRC Press. This book was released on 2007-08-27 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integrating various technologies with informational systems provides vast improvements to the overall research and development that occur in the biopharmaceutical industry. One of the first books to explore this area, Functional Informatics in Drug Discovery examines all aspects of technology integration and information flow in a biopharmaceutical

Download or read book Parallel Projected Variable Metric Algorithms for Unconstrained Optimization written by Institute for Computer Applications in Science and Engineering and published by . This book was released on 1989 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Linear and Nonlinear Optimization written by Richard W. Cottle and published by Springer. This book was released on 2017-06-11 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: ​This textbook on Linear and Nonlinear Optimization is intended for graduate and advanced undergraduate students in operations research and related fields. It is both literate and mathematically strong, yet requires no prior course in optimization. As suggested by its title, the book is divided into two parts covering in their individual chapters LP Models and Applications; Linear Equations and Inequalities; The Simplex Algorithm; Simplex Algorithm Continued; Duality and the Dual Simplex Algorithm; Postoptimality Analyses; Computational Considerations; Nonlinear (NLP) Models and Applications; Unconstrained Optimization; Descent Methods; Optimality Conditions; Problems with Linear Constraints; Problems with Nonlinear Constraints; Interior-Point Methods; and an Appendix covering Mathematical Concepts. Each chapter ends with a set of exercises. The book is based on lecture notes the authors have used in numerous optimization courses the authors have taught at Stanford University. It emphasizes modeling and numerical algorithms for optimization with continuous (not integer) variables. The discussion presents the underlying theory without always focusing on formal mathematical proofs (which can be found in cited references). Another feature of this book is its inclusion of cultural and historical matters, most often appearing among the footnotes. "This book is a real gem. The authors do a masterful job of rigorously presenting all of the relevant theory clearly and concisely while managing to avoid unnecessary tedious mathematical details. This is an ideal book for teaching a one or two semester masters-level course in optimization – it broadly covers linear and nonlinear programming effectively balancing modeling, algorithmic theory, computation, implementation, illuminating historical facts, and numerous interesting examples and exercises. Due to the clarity of the exposition, this book also serves as a valuable reference for self-study." Professor Ilan Adler, IEOR Department, UC Berkeley "A carefully crafted introduction to the main elements and applications of mathematical optimization. This volume presents the essential concepts of linear and nonlinear programming in an accessible format filled with anecdotes, examples, and exercises that bring the topic to life. The authors plumb their decades of experience in optimization to provide an enriching layer of historical context. Suitable for advanced undergraduates and masters students in management science, operations research, and related fields." Michael P. Friedlander, IBM Professor of Computer Science, Professor of Mathematics, University of British Columbia

Download or read book Parallel Methods for Unconstrained Optimization written by Charles Herbert Still and published by . This book was released on 1990 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematical Theory of Optimization written by Ding-Zhu Du and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the mathematical theory of optimization. It emphasizes the convergence theory of nonlinear optimization algorithms and applications of nonlinear optimization to combinatorial optimization. Mathematical Theory of Optimization includes recent developments in global convergence, the Powell conjecture, semidefinite programming, and relaxation techniques for designs of approximation solutions of combinatorial optimization problems.

Download or read book Computational Methods for Optimal Design and Control written by J. Borggaard and published by Springer Science & Business Media. This book was released on 1998-10-23 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Second International Workshop on Optimal Design and Control, held in Arlington, Virginia, 30 September-3 Octo ber, 1997. The First Workshop was held in Blacksburg, Virginia in 1994. The proceedings of that meeting also appeared in the Birkhauser series on Progress in Systems and Control Theory and may be obtained through Birkhauser. These workshops were sponsored by the Air Force Office of Scientific Re search through the Center for Optimal Design and Control (CODAC) at Vrrginia Tech. The meetings provided a forum for the exchange of new ideas and were designed to bring together diverse viewpoints and to highlight new applications. The primary goal of the workshops was to assess the current status of research and to analyze future directions in optimization based design and control. The present volume contains the technical papers presented at the Second Workshop. More than 65 participants from 6 countries attended the meeting and contributed to its success. It has long been recognized that many modern optimal design problems are best viewed as variational and optimal control problems. Indeed, the famous problem of determining the body of revolution that produces a minimum drag nose shape in hypersonic How was first proposed by Newton in 1686. Optimal control approaches to design can provide theoretical and computational insight into these problems. This volume contains a number of papers which deal with computational aspects of optimal control.

Download or read book Parallel Non gradient Algorithms for Unconstrained Optimisation written by Keramatalla Bassiri and published by . This book was released on 1996 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Computational Science ICCS 2021 written by Maciej Paszynski and published by Springer Nature. This book was released on 2021-06-09 with total page 722 pages. Available in PDF, EPUB and Kindle. Book excerpt: The six-volume set LNCS 12742, 12743, 12744, 12745, 12746, and 12747 constitutes the proceedings of the 21st International Conference on Computational Science, ICCS 2021, held in Krakow, Poland, in June 2021.* The total of 260 full papers and 57 short papers presented in this book set were carefully reviewed and selected from 635 submissions. 48 full and 14 short papers were accepted to the main track from 156 submissions; 212 full and 43 short papers were accepted to the workshops/ thematic tracks from 479 submissions. The papers were organized in topical sections named: Part I: ICCS Main Track Part II: Advances in High-Performance Computational Earth Sciences: Applications and Frameworks; Applications of Computational Methods in Artificial Intelligence and Machine Learning; Artificial Intelligence and High-Performance Computing for Advanced Simulations; Biomedical and Bioinformatics Challenges for Computer Science Part III: Classifier Learning from Difficult Data; Computational Analysis of Complex Social Systems; Computational Collective Intelligence; Computational Health Part IV: Computational Methods for Emerging Problems in (dis-)Information Analysis; Computational Methods in Smart Agriculture; Computational Optimization, Modelling and Simulation; Computational Science in IoT and Smart Systems Part V: Computer Graphics, Image Processing and Artificial Intelligence; Data-Driven Computational Sciences; Machine Learning and Data Assimilation for Dynamical Systems; MeshFree Methods and Radial Basis Functions in Computational Sciences; Multiscale Modelling and Simulation Part VI: Quantum Computing Workshop; Simulations of Flow and Transport: Modeling, Algorithms and Computation; Smart Systems: Bringing Together Computer Vision, Sensor Networks and Machine Learning; Software Engineering for Computational Science; Solving Problems with Uncertainty; Teaching Computational Science; Uncertainty Quantification for Computational Models *The conference was held virtually.

Download or read book Parallel Competing Algorithms in Global Optimization written by Hermanus Petrus Johannes Bolton and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Specialized techniques are needed to solve global optimization problems, due to the existence of multiple local optima or numerical noise in the objective function. The complexity of the problem is aggravated when discontinuities and constraints are present, or when evaluation of the objective function is computationally expensive. The global (minimization) programming problem is defined as finding the variable set for which the objective function obtains not only a local minimum, but also the smallest value, the global minimum. From a mathematical point of view, the global programming problem is essentially unsolvable, due to a lack of mathematical conditions characterizing the global optimum. In this study, the unconstrained global programming problem is addressed using a number of novel heuristic approaches. Firstly, a probabilistic global stopping criterion is presented for multi-start algorithms. This rule, denoted the unified Bayesian stopping criterion, is based on the single mild assumption that the probability of convergence to the global minimum is comparable to the probability of convergence to any other local minimum. This rule was previously presented for use in combination with a specific global optimization algorithm, and is now shown to be effective when used in a general multi-start approach. The suitability of the unified Bayesian stopping criterion is demonstrated for a number of algorithms using standard test functions. Secondly, multi-start global optimization algorithms based on multiple local searches, com bined with the unified Bayesian stopping criterion, are presented. Numerical results reveal that these simple multi-start algorithms outperform a number of leading contenders. Thirdly, parallelization of the sequential multi-start algorithms is shown to effectively re duce the apparent computational time associated with solving expensive global programming problems. Fourthly, two algorithms simulating natural phenomena are implemented, namely the rel atively new particle swarm optimization method and the well known genetic algorithm. For the current implementations, numerical results indicate that the computational effort associated with these methods is comparable. Fifthly, the observation that no single global optimization algorithm can consistently out perform any other algorithm when a large set of problems is considered, leads to the de velopment of a parallel competing algorithm infrastructure. In this infrastructure different algorithms, ranging from deterministic to stochastic, compete simultaneously for a contri bution to the unified Bayesian global stopping criterion. This is an important step towards facilitating an infrastructure that is suitable for a range of problems in different classes. In the sixth place, the constrained global programming problems is addressed using con strained algorithms in the parallel competing algorithm infrastructure. The developed methods are extensively tested using standard test functions, for both serial and parallel implementations. An optimization procedure is also presented to solve the slope stability problem faced in civil engineering. This new procedure determines the factor of safety of slopes using a global optimization approach.

Download or read book Parallel Algorithms for Unconstrained and Constrained Nonlinear Optimization written by F. A. Lootsma and published by . This book was released on 1986 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: