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Author: J Lopez
Publisher:
ISBN: 9781099794346
Category :
Languages : en
Pages : 388
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Book Description
Optimization Toolbox provides functions for finding parameters that minimize or maximize objectives while satisfying constraints. The toolbox includes solvers for linear programming (LP), mixed-integer linear programming (MILP), quadratic programming(QP), nonlinear programming (NLP), constrained linear least squares, nonlinear least squares, and nonlinear equations. You can define your optimization problem with functions and matrices or by specifying variable expressions that reflect the underlying mathematics. You can use the toolbox solvers to fin optimal solutions to continuous and discrete problems, perform trade of analyses, and incorporate optimization methods into algorithms and applications. The toolbox lets you perform design optimization tasks, including parameter estimation, component selection, and parameter tuning. It can be used to fin optimal solutions in applications such as portfolio optimization, resource allocation, and production planning and scheduling.Key Features-Nonlinear and multiobjective optimization of smooth constrained and unconstrained problems-Solvers for nonlinear least squares, constrained linear least squares, data fitting and nonlinear equations-Quadratic programming (QP) and linear programming (LP)-Mixed-integer linear programming (MILP)-Optimization modeling tools-Graphical monitoring of optimization progress-Gradient estimation acceleration (with Parallel Computing Toolbox(TM))
Author: J Lopez
Publisher:
ISBN: 9781099794346
Category :
Languages : en
Pages : 388
Get Book Here
Book Description
Optimization Toolbox provides functions for finding parameters that minimize or maximize objectives while satisfying constraints. The toolbox includes solvers for linear programming (LP), mixed-integer linear programming (MILP), quadratic programming(QP), nonlinear programming (NLP), constrained linear least squares, nonlinear least squares, and nonlinear equations. You can define your optimization problem with functions and matrices or by specifying variable expressions that reflect the underlying mathematics. You can use the toolbox solvers to fin optimal solutions to continuous and discrete problems, perform trade of analyses, and incorporate optimization methods into algorithms and applications. The toolbox lets you perform design optimization tasks, including parameter estimation, component selection, and parameter tuning. It can be used to fin optimal solutions in applications such as portfolio optimization, resource allocation, and production planning and scheduling.Key Features-Nonlinear and multiobjective optimization of smooth constrained and unconstrained problems-Solvers for nonlinear least squares, constrained linear least squares, data fitting and nonlinear equations-Quadratic programming (QP) and linear programming (LP)-Mixed-integer linear programming (MILP)-Optimization modeling tools-Graphical monitoring of optimization progress-Gradient estimation acceleration (with Parallel Computing Toolbox(TM))
Author: Kaisa Miettinen
Publisher: Springer Science & Business Media
ISBN: 1461555639
Category : Business & Economics
Languages : en
Pages : 304
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Book Description
Problems with multiple objectives and criteria are generally known as multiple criteria optimization or multiple criteria decision-making (MCDM) problems. So far, these types of problems have typically been modelled and solved by means of linear programming. However, many real-life phenomena are of a nonlinear nature, which is why we need tools for nonlinear programming capable of handling several conflicting or incommensurable objectives. In this case, methods of traditional single objective optimization and linear programming are not enough; we need new ways of thinking, new concepts, and new methods - nonlinear multiobjective optimization. Nonlinear Multiobjective Optimization provides an extensive, up-to-date, self-contained and consistent survey, review of the literature and of the state of the art on nonlinear (deterministic) multiobjective optimization, its methods, its theory and its background. The amount of literature on multiobjective optimization is immense. The treatment in this book is based on approximately 1500 publications in English printed mainly after the year 1980. Problems related to real-life applications often contain irregularities and nonsmoothnesses. The treatment of nondifferentiable multiobjective optimization in the literature is rather rare. For this reason, this book contains material about the possibilities, background, theory and methods of nondifferentiable multiobjective optimization as well. This book is intended for both researchers and students in the areas of (applied) mathematics, engineering, economics, operations research and management science; it is meant for both professionals and practitioners in many different fields of application. The intention has been to provide a consistent summary that may help in selecting an appropriate method for the problem to be solved. It is hoped the extensive bibliography will be of value to researchers.
Author: Perez C.
Publisher:
ISBN: 9781974587209
Category :
Languages : en
Pages : 278
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Book Description
The generalization of optimization theory and techniques to other formulations comprises a large area of applied mathematics. Optimization includes finding "best available" values of some objective function given a defined domain (or input), including a variety of different types of objective functions and different types of domains.Adding more than one objective to an optimization problem adds complexity. For example, to optimize a structural design, one would desire a design that is both light and rigid. When two objectives conflict, a trade-off must be created. There may be one lightest design, one stiffest design, and an infinite number of designs that are some compromise of weight and rigidity. The set of trade-off designs that cannot be improved upon according to one criterion without hurting another criterion is known as the Pareto set. The curve created plotting weight against stiffness of the best designs is known as the Pareto frontier.A design is judged to be "Pareto optimal" (equivalently, "Pareto efficient" or in the Pareto set) if it is not dominated by any other design: If it is worse than another design in some respects and no better in any respect, then it is dominated and is not Pareto optimal. The choice among "Pareto optimal" solutions to determine the "favorite solution" is delegated to the decision maker. In other words, defining the problem as multi-objective optimization signals that some information is missing: desirable objectives are given but combinations of them are not rated relative to each other. In some cases, the missing information can be derived by interactive sessions with the decision maker.Multi-objective optimization problems have been generalized further into vector optimization problems where the (partial) ordering is no longer given by the Pareto ordering.Optimization problems are often multi-modal; that is, they possess multiple good solutions. They could all be globally good or there could be a mix of globally good and locally good solutions. Obtaining all (or at least some of) the multiple solutions is the goal of a multi-modal optimizer.Classical optimization techniques due to their iterative approach do not perform satisfactorily when they are used to obtain multiple solutions, since it is not guaranteed that different solutions will be obtained even with different starting points in multiple runs of the algorithm. Evolutionary algorithms, however, are a very popular approach to obtain multiple solutions in a multi-modal optimization task.This book develops the following topics:* "Multiobjective Optimization Algorithms" * "Using fminimax with a Simulink Model" * "Signal Processing Using fgoalattain" * "Generate and Plot a Pareto Front" * "Linear Programming Algorithms" * "Maximize Long-Term Investments Using Linear Programming" * "Mixed-Integer Linear Programming Algorithms" * "Tuning Integer Linear Programming" * "Mixed-Integer Linear Programming Basics" * "Optimal Dispatch of Power Generators" * "Mixed-Integer Quadratic Programming Portfolio Optimization" * "Quadratic Programming Algorithms"* "Quadratic Minimization with Bound Constraints" * "Quadratic Minimization with Dense, Structured Hessian"* "Large Sparse Quadratic Program with Interior Point Algorithm" * "Least-Squares (Model Fitting) Algorithms" * "lsqnonlin with a Simulink Model" * "Nonlinear Least Squares With and Without Jacobian" * "Linear Least Squares with Bound Constraints" * "Optimization App with the lsqlin Solver" * "Maximize Long-Term Investments Using Linear Programming" * "Jacobian Multiply Function with Linear Least Squares" * "Nonlinear Curve Fitting with lsqcurvefit" * "Fit a Model to Complex-Valued Data" * "Systems of Equations" * "Nonlinear Equations with Analytic Jacobian" * "Nonlinear Equations with Jacobian" * "Nonlinear Equations with Jacobian Sparsity Pattern"* "Nonlinear Systems with Constraints" * "Parallel Computing for Optimization"
Author: N. Foster
Publisher:
ISBN: 9781520265025
Category :
Languages : en
Pages : 270
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Book Description
MATLAB Optimization Toolbox provides widely used algorithms for and large-scale optimization. These algorithms solve constrained and unconstrained continuous and discrete problems. The toolbox, developed in this book, includes functions for linear programming, quadratic programming, binary integer programming, nonlinear optimization, nonlinear least squares, systems of nonlinear equations, and multiobjective optimization. You can use them to find optimal solutions, perform tradeoff analyses, balance multiple design alternatives, and incorporate optimization methods into algorithms and models. This books develops the optimization functions in MATLAB and presents examples.
Author: Dingyü Xue
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110667010
Category : Computers
Languages : en
Pages : 342
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Book Description
This book focuses on solving optimization problems with MATLAB. Descriptions and solutions of nonlinear equations of any form are studied first. Focuses are made on the solutions of various types of optimization problems, including unconstrained and constrained optimizations, mixed integer, multiobjective and dynamic programming problems. Comparative studies and conclusions on intelligent global solvers are also provided.
Author: E. Clapton
Publisher: Createspace Independent Publishing Platform
ISBN: 9781540349972
Category :
Languages : en
Pages : 292
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Book Description
MATLAB Optimization Toolbox provides widely used algorithms for and large-scale optimization. These algorithms solve constrained and unconstrained continuous and discrete problems. The toolbox, developed in this book, includes functions for linear programming, quadratic programming, binary integer programming, nonlinear optimization, nonlinear least squares, systems of nonlinear equations, and multiobjective optimization. You can use them to find optimal solutions, perform tradeoff analyses, balance multiple design alternatives, and incorporate optimization methods into algorithms and models.The more important features are the next:* Interactive tools for defining and solving optimization problems and monitoring solution progress* Solvers for nonlinear and multiobjective optimization * Solvers for nonlinear least squares, data fitting, and nonlinear equations* Methods for solving quadratic and linear programming problems * Methods for solving binary integer programming problems* Parallel computing support in selected constrained nonlinear solvers
Author: Clapton E.
Publisher: Createspace Independent Publishing Platform
ISBN: 9781540331861
Category :
Languages : en
Pages : 204
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Book Description
MATLAB Optimization Toolbox provides widely used algorithms for and large-scale optimization. These algorithms solve constrained and unconstrained continuous and discrete problems. The toolbox, developed in this book, includes functions for linear programming, quadratic programming, binary integer programming, nonlinear optimization, nonlinear least squares, systems of nonlinear equations, and multiobjective optimization. You can use them to find optimal solutions, perform tradeoff analyses, balance multiple design alternatives, and incorporate optimization methods into algorithms and models.
Author: Claus Hillermeier
Publisher: Birkhäuser
ISBN: 3034882807
Category : Mathematics
Languages : en
Pages : 139
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Book Description
Arguably, many industrial optimization problems are of the multiobjective type. The present work, after providing a survey of the state of the art in multiobjective optimization, gives new insight into this important mathematical field by consequently taking up the viewpoint of differential geometry. This approach, unprecedented in the literature, very naturally results in a generalized homotopy method for multiobjective optimization which is theoretically well-founded and numerically efficient. The power of the new method is demonstrated by solving two real-life problems of industrial optimization. The book presents recent results obtained by the author and is aimed at mathematicians, scientists, students and practitioners interested in optimization and numerical homotopy methods.
Author: Achille Messac
Publisher: Cambridge University Press
ISBN: 1316381374
Category : Technology & Engineering
Languages : en
Pages : 503
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Book Description
Optimization in Practice with MATLAB® provides a unique approach to optimization education. It is accessible to both junior and senior undergraduate and graduate students, as well as industry practitioners. It provides a strongly practical perspective that allows the student to be ready to use optimization in the workplace. It covers traditional materials, as well as important topics previously unavailable in optimization books (e.g. numerical essentials - for successful optimization). Written with both the reader and the instructor in mind, Optimization in Practice with MATLAB® provides practical applications of real-world problems using MATLAB®, with a suite of practical examples and exercises that help the students link the theoretical, the analytical, and the computational in each chapter. Additionally, supporting MATLAB® m-files are available for download via www.cambridge.org.messac. Lastly, adopting instructors will receive a comprehensive solution manual with solution codes along with lectures in PowerPoint with animations for each chapter, and the text's unique flexibility enables instructors to structure one- or two-semester courses.
Author: Amir Beck
Publisher: SIAM
ISBN: 1611973643
Category : Mathematics
Languages : en
Pages : 286
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Book Description
This book provides the foundations of the theory of nonlinear optimization as well as some related algorithms and presents a variety of applications from diverse areas of applied sciences. The author combines three pillars of optimization?theoretical and algorithmic foundation, familiarity with various applications, and the ability to apply the theory and algorithms on actual problems?and rigorously and gradually builds the connection between theory, algorithms, applications, and implementation. Readers will find more than 170 theoretical, algorithmic, and numerical exercises that deepen and enhance the reader's understanding of the topics. The author includes offers several subjects not typically found in optimization books?for example, optimality conditions in sparsity-constrained optimization, hidden convexity, and total least squares. The book also offers a large number of applications discussed theoretically and algorithmically, such as circle fitting, Chebyshev center, the Fermat?Weber problem, denoising, clustering, total least squares, and orthogonal regression and theoretical and algorithmic topics demonstrated by the MATLAB? toolbox CVX and a package of m-files that is posted on the book?s web site.
