Algorithms For Derivative Free Optimization
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Introduction To Derivative Free Optimization
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Author : Andrew R. Conn
language : en
Publisher: SIAM
Release Date : 2009-04-16
Introduction To Derivative Free Optimization written by Andrew R. Conn and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-16 with Mathematics categories.
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.
Derivative Free Optimization
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Author : Yang Yu
language : en
Publisher: Springer Nature
Release Date : 2025-08-03
Derivative Free Optimization written by Yang Yu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-03 with Mathematics categories.
This book offers a pioneering exploration of classification-based derivative-free optimization (DFO), providing researchers and professionals in artificial intelligence, machine learning, AutoML, and optimization with a robust framework for addressing complex, large-scale problems where gradients are unavailable. By bridging theoretical foundations with practical implementations, it fills critical gaps in the field, making it an indispensable resource for both academic and industrial audiences. The book introduces innovative frameworks such as sampling-and-classification (SAC) and sampling-and-learning (SAL), which underpin cutting-edge algorithms like Racos and SRacos. These methods are designed to excel in challenging optimization scenarios, including high-dimensional search spaces, noisy environments, and parallel computing. A dedicated section on the ZOOpt toolbox provides practical tools for implementing these algorithms effectively. The book’s structure moves from foundational principles and algorithmic development to advanced topics and real-world applications, such as hyperparameter tuning, neural architecture search, and algorithm selection in AutoML. Readers will benefit from a comprehensive yet concise presentation of modern DFO methods, gaining theoretical insights and practical tools to enhance their research and problem-solving capabilities. A foundational understanding of machine learning, probability theory, and algorithms is recommended for readers to fully engage with the material.
Algorithms For Derivative Free Optimization
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Author : Luis Miguel Rios
language : en
Publisher: ProQuest
Release Date : 2009
Algorithms For Derivative Free Optimization written by Luis Miguel Rios and has been published by ProQuest this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
Fueled by a growing number of applications in science and engineering, the development of derivative-free optimization algorithms has long been studied and found renewed interest. The problem addressed is the optimization of a deterministic function f : Rn→ R over a domain of interest that possibly includes constraints g(x) ≤ 0, with g : Rn→ Rm . We assume that the derivatives of f and g are neither symbolically available nor numerically computable, and that bounds, such as Lipschitz constants, for the derivatives of f and g are also unavailable.
Derivative Free And Blackbox Optimization
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Author : Charles Audet
language : en
Publisher: Springer
Release Date : 2017-12-02
Derivative Free And Blackbox Optimization written by Charles Audet and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-02 with Mathematics categories.
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.
Derivative Free Optimization Algorithms For Computationally Expensive Functions
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Author : Stefan Martin Wild
language : en
Publisher:
Release Date : 2009
Derivative Free Optimization Algorithms For Computationally Expensive Functions written by Stefan Martin Wild and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
This thesis concerns the development and analysis of derivative-free optimization algorithms for simulation-based functions that are computationally expensive to evaluate. The first contribution is the introduction of data profiles as a tool for analyzing the performance of derivative-free optimization solvers when constrained by a computational budget. Using these profiles, together with a convergence test that measures the decrease in function value, we find that on three different sets of test problems, a model-based solver performs better than the two direct search solvers tested. The next contribution is a new model-based derivative-free algorithm, ORBIT, for unconstrained local optimization. A trust-region framework using interpolating Radial Basis Function (RBF) models is employed. RBF models allow ORBIT to interpolate nonlinear functions using fewer function evaluations than many of the polynomial models considered by present techniques. We provide an analysis of the approximation guarantees obtained by interpolating the function at a set of sufficiently affinely independent points. We detail necessary and sufficient conditions that an RBF model must obey to fit within our framework and prove that this framework allows for convergence to first-order critical points. We present numerical results on test problems as well as three application problems from environmental engineering to support ORBIT's effectiveness when relatively few func- tion evaluations are available. The framework used by ORBIT is also extended to include other models, in particular undetermined interpolating quadratics. These quadratics are flexible in their ability to interpolate at dynamic numbers of previously evaluated points. The third contribution is a new multistart global optimization algorithm, GORBIT, that takes advantage of the expensive function evaluations done in the course of both the global exploration and local refinement phases. We modify ORBIT to handle both bound constraints and external functional evaluations and use it as the local solver. For the global exploration phase, a new procedure for making maximum use of the information from previous evaluations, MIPE, is introduced. Numerical tests motivating our approach are presented and we illustrate using GORBIT on the problem of finding error-prone systems for Gaussian elimination.
A Derivative Free Two Level Random Search Method For Unconstrained Optimization
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Author : Neculai Andrei
language : en
Publisher:
Release Date : 2021
A Derivative Free Two Level Random Search Method For Unconstrained Optimization written by Neculai Andrei and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Electronic books categories.
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.
Derivative Free Direct Type Global Optimization
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Author : Linas Stripinis
language : en
Publisher: Springer Nature
Release Date : 2023-11-27
Derivative Free Direct Type Global Optimization written by Linas Stripinis and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-27 with Mathematics categories.
After providing an in-depth introduction to derivative-free global optimization with various constraints, this book presents new original results from well-known experts on the subject. A primary focus of this book is the well-known class of deterministic DIRECT (DIviding RECTangle)-type algorithms. This book describes a new set of algorithms derived from newly developed partitioning, sampling, and selection approaches in the box- and generally-constrained global optimization, including extensions to multi-objective optimization. DIRECT-type optimization algorithms are discussed in terms of fundamental principles, potential, and boundaries of their applicability. The algorithms are analyzed from various perspectives to offer insight into their main features. This explains how and why they are effective at solving optimization problems. As part of this book, the authors also present several techniques for accelerating the DIRECT-type algorithms through parallelization and implementing efficient data structures by revealing the pros and cons of the design challenges involved. A collection of DIRECT-type algorithms described and analyzed in this book is available in DIRECTGO, a MATLAB toolbox on GitHub. Lastly, the authors demonstrate the performance of the algorithms for solving a wide range of global optimization problems with various constraints ranging from a few to hundreds of variables. Additionally, well-known practical problems from the literature are used to demonstrate the effectiveness of the developed algorithms. It is evident from these numerical results that the newly developed approaches are capable of solving problems with a wide variety of structures and complexity levels. Since implementations of the algorithms are publicly available, this monograph is full of examples showing how to use them and how to choose the most efficient ones, depending on the nature of the problem being solved. Therefore, many specialists, students, researchers, engineers, economists, computer scientists, operations researchers, and others will find this book interesting and helpful.
Analysis And Development Of Surrogate Assisted Derivative Free Optimization Algorithms
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Author : 林雨亭
language : en
Publisher:
Release Date : 2009
Analysis And Development Of Surrogate Assisted Derivative Free Optimization Algorithms written by 林雨亭 and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
Derivative Free Optimization Algorithms For Mesh Quality Improvement
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Author : Jeonghyung Park
language : en
Publisher:
Release Date : 2009
Derivative Free Optimization Algorithms For Mesh Quality Improvement written by Jeonghyung Park and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
Simulation Based Optimization
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Author : Geng Deng
language : en
Publisher:
Release Date : 2007
Simulation Based Optimization written by Geng Deng and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.