A Derivative Free Two Level Random Search Method For Unconstrained Optimization PDF Download
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| Author | : Neculai Andrei |
| Publisher | : Springer Nature |
| Total Pages | : 126 |
| Release | : 2021-03-31 |
| Genre | : Mathematics |
| ISBN | : 3030685179 |
Download A Derivative-free Two Level Random Search Method for Unconstrained Optimization Book in PDF, ePub and Kindle
The book is intended for graduate students and researchers in mathematics, computer science, and operational research. The book presents a new derivative-free optimization method/algorithm based on randomly generated trial points in specified domains and where the best ones are selected at each iteration by using a number of rules. This method is different from many other well established methods presented in the literature and proves to be competitive for solving many unconstrained optimization problems with different structures and complexities, with a relative large number of variables. Intensive numerical experiments with 140 unconstrained optimization problems, with up to 500 variables, have shown that this approach is efficient and robust. Structured into 4 chapters, Chapter 1 is introductory. Chapter 2 is dedicated to presenting a two level derivative-free random search method for unconstrained optimization. It is assumed that the minimizing function is continuous, lower bounded and its minimum value is known. Chapter 3 proves the convergence of the algorithm. In Chapter 4, the numerical performances of the algorithm are shown for solving 140 unconstrained optimization problems, out of which 16 are real applications. This shows that the optimization process has two phases: the reduction phase and the stalling one. Finally, the performances of the algorithm for solving a number of 30 large-scale unconstrained optimization problems up to 500 variables are presented. These numerical results show that this approach based on the two level random search method for unconstrained optimization is able to solve a large diversity of problems with different structures and complexities. There are a number of open problems which refer to the following aspects: the selection of the number of trial or the number of the local trial points, the selection of the bounds of the domains where the trial points and the local trial points are randomly generated and a criterion for initiating the line search.
| Author | : Neculai Andrei |
| Publisher | : Springer Nature |
| Total Pages | : 824 |
| Release | : 2022-10-18 |
| Genre | : Mathematics |
| ISBN | : 3031087208 |
Download Modern Numerical Nonlinear Optimization Book in PDF, ePub and Kindle
This book includes a thorough theoretical and computational analysis of unconstrained and constrained optimization algorithms and combines and integrates the most recent techniques and advanced computational linear algebra methods. Nonlinear optimization methods and techniques have reached their maturity and an abundance of optimization algorithms are available for which both the convergence properties and the numerical performances are known. This clear, friendly, and rigorous exposition discusses the theory behind the nonlinear optimization algorithms for understanding their properties and their convergence, enabling the reader to prove the convergence of his/her own algorithms. It covers cases and computational performances of the most known modern nonlinear optimization algorithms that solve collections of unconstrained and constrained optimization test problems with different structures, complexities, as well as those with large-scale real applications. The book is addressed to all those interested in developing and using new advanced techniques for solving large-scale unconstrained or constrained complex optimization problems. Mathematical programming researchers, theoreticians and practitioners in operations research, practitioners in engineering and industry researchers, as well as graduate students in mathematics, Ph.D. and master in mathematical programming will find plenty of recent information and practical approaches for solving real large-scale optimization problems and applications.
| Author | : Charles Audet |
| Publisher | : Springer |
| Total Pages | : 307 |
| Release | : 2017-12-02 |
| Genre | : Mathematics |
| ISBN | : 3319689134 |
Download Derivative-Free and Blackbox Optimization Book in PDF, ePub and Kindle
This book is designed as a textbook, suitable for self-learning or for teaching an upper-year university course on derivative-free and blackbox optimization. The book is split into 5 parts and is designed to be modular; any individual part depends only on the material in Part I. Part I of the book discusses what is meant by Derivative-Free and Blackbox Optimization, provides background material, and early basics while Part II focuses on heuristic methods (Genetic Algorithms and Nelder-Mead). Part III presents direct search methods (Generalized Pattern Search and Mesh Adaptive Direct Search) and Part IV focuses on model-based methods (Simplex Gradient and Trust Region). Part V discusses dealing with constraints, using surrogates, and bi-objective optimization. End of chapter exercises are included throughout as well as 15 end of chapter projects and over 40 figures. Benchmarking techniques are also presented in the appendix.
| Author | : C. T. Kelley |
| Publisher | : SIAM |
| Total Pages | : 171 |
| Release | : 2011-09-29 |
| Genre | : Mathematics |
| ISBN | : 1611971896 |
Download Implicit Filtering Book in PDF, ePub and Kindle
A description of the implicit filtering algorithm, its convergence theory and a new MATLAB® implementation.
| Author | : Jorge Nocedal |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 686 |
| Release | : 2006-12-11 |
| Genre | : Mathematics |
| ISBN | : 0387400656 |
Download Numerical Optimization Book in PDF, ePub and Kindle
Optimization is an important tool used in decision science and for the analysis of physical systems used in engineering. One can trace its roots to the Calculus of Variations and the work of Euler and Lagrange. This natural and reasonable approach to mathematical programming covers numerical methods for finite-dimensional optimization problems. It begins with very simple ideas progressing through more complicated concepts, concentrating on methods for both unconstrained and constrained optimization.
| Author | : Andrew R. Conn |
| Publisher | : SIAM |
| Total Pages | : 276 |
| Release | : 2009-04-16 |
| Genre | : Mathematics |
| ISBN | : 0898716683 |
Download Introduction to Derivative-Free Optimization Book in PDF, ePub and Kindle
The first contemporary comprehensive treatment of optimization without derivatives. This text explains how sampling and model techniques are used in derivative-free methods and how they are designed to solve optimization problems. It is designed to be readily accessible to both researchers and those with a modest background in computational mathematics.
| Author | : Mykel J. Kochenderfer |
| Publisher | : MIT Press |
| Total Pages | : 521 |
| Release | : 2019-03-12 |
| Genre | : Computers |
| ISBN | : 0262039427 |
Download Algorithms for Optimization Book in PDF, ePub and Kindle
A comprehensive introduction to optimization with a focus on practical algorithms for the design of engineering systems. This book offers a comprehensive introduction to optimization with a focus on practical algorithms. The book approaches optimization from an engineering perspective, where the objective is to design a system that optimizes a set of metrics subject to constraints. Readers will learn about computational approaches for a range of challenges, including searching high-dimensional spaces, handling problems where there are multiple competing objectives, and accommodating uncertainty in the metrics. Figures, examples, and exercises convey the intuition behind the mathematical approaches. The text provides concrete implementations in the Julia programming language. Topics covered include derivatives and their generalization to multiple dimensions; local descent and first- and second-order methods that inform local descent; stochastic methods, which introduce randomness into the optimization process; linear constrained optimization, when both the objective function and the constraints are linear; surrogate models, probabilistic surrogate models, and using probabilistic surrogate models to guide optimization; optimization under uncertainty; uncertainty propagation; expression optimization; and multidisciplinary design optimization. Appendixes offer an introduction to the Julia language, test functions for evaluating algorithm performance, and mathematical concepts used in the derivation and analysis of the optimization methods discussed in the text. The book can be used by advanced undergraduates and graduate students in mathematics, statistics, computer science, any engineering field, (including electrical engineering and aerospace engineering), and operations research, and as a reference for professionals.
| Author | : Joaquim R. R. A. Martins |
| Publisher | : Cambridge University Press |
| Total Pages | : 653 |
| Release | : 2021-11-18 |
| Genre | : Mathematics |
| ISBN | : 110898861X |
Download Engineering Design Optimization Book in PDF, ePub and Kindle
Based on course-tested material, this rigorous yet accessible graduate textbook covers both fundamental and advanced optimization theory and algorithms. It covers a wide range of numerical methods and topics, including both gradient-based and gradient-free algorithms, multidisciplinary design optimization, and uncertainty, with instruction on how to determine which algorithm should be used for a given application. It also provides an overview of models and how to prepare them for use with numerical optimization, including derivative computation. Over 400 high-quality visualizations and numerous examples facilitate understanding of the theory, and practical tips address common issues encountered in practical engineering design optimization and how to address them. Numerous end-of-chapter homework problems, progressing in difficulty, help put knowledge into practice. Accompanied online by a solutions manual for instructors and source code for problems, this is ideal for a one- or two-semester graduate course on optimization in aerospace, civil, mechanical, electrical, and chemical engineering departments.
| Author | : Ding-Zhu Du |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 277 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 1475757956 |
Download Mathematical Theory of Optimization Book in PDF, ePub and Kindle
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.
| Author | : L. Ashok Kumar |
| Publisher | : CRC Press |
| Total Pages | : 454 |
| Release | : 2018-11-15 |
| Genre | : Mathematics |
| ISBN | : 0429809913 |
Download Computational Paradigm Techniques for Enhancing Electric Power Quality Book in PDF, ePub and Kindle
This book focusses on power quality improvement and enhancement techniques with aid of intelligent controllers and experimental results. It covers topics ranging from the fundamentals of power quality indices, mitigation methods, advanced controller design and its step by step approach, simulation of the proposed controllers for real time applications and its corresponding experimental results, performance improvement paradigms and its overall analysis, which helps readers understand power quality from its fundamental to experimental implementations. The book also covers implementation of power quality improvement practices. Key Features Provides solution for the power quality improvement with intelligent techniques Incorporated and Illustrated with simulation and experimental results Discusses renewable energy integration and multiple case studies pertaining to various loads Combines the power quality literature with power electronics based solutions Includes implementation examples, datasets, experimental and simulation procedures
