[PDF] Operations Research Optimization Functions In Matlab For Linear And Nonlinear Programming eBook

Author : Perez C.
Publisher :
Page : 316 pages
File Size : 48,63 MB
Release : 2017-08-16
Category :
ISBN : 9781974585328

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In mathematics, computer science and operations research, mathematical optimization, also spelled mathematical optimisation (alternatively named mathematical programming or simply optimization or optimisation), is the selection of a best element (with regard to some criterion) from some set of available alternatives.In the simplest case, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations comprises a large area of applied mathematics. More generally, 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.MATLAB Optimization Toolbox provides functions for finding parameters that minimize or maximize objectives while satisfying constraints. The toolbox includes solvers for linear programming, mixed-integer linear programming, quadratic programming, nonlinear optimization, and nonlinear least squares. You can use these solvers to find optimal solutions to continuous and discrete problems, perform tradeoff analyses, and incorporate optimization methods into algorithms and applications.This book develops the following topics:* "Linear Programming" * "Nonlinear Programming" * "Constrained Linear and Nonlinear Problem" * "Optimization Toolbox Solvers" * "Optimization Decision Table" * "fmincon Algorithms" * "fsolve Algorithms"* "fminunc Algorithms"* "Least Squares Algorithms"* "Linear Programming Algorithms"* "Quadratic Programming Algorithms"* "Large-Scale vs. Medium-Scale Algorithms"* "Potential Inaccuracy with Interior-Point Algorithms"* "Edit Optimization Parameters" * "Complex Numbers in Optimization Toolbox Solvers" * "Scalar Objective Functions" * "Vector and Matrix Objective Functions" * "Objective Functions for Linear or Quadratic Problems" * "Maximizing an Objective"* "Bound Constraints" * "Linear an Nonlinlear Constraints"* "optimoptions and optimset" * "Tolerances and Stopping Criteria"* "Checking Validity of Gradients or Jacobians"* "Iterations and Function Counts" * "First-Order Optimality Measure" * "Lagrange Multiplier Structures" * "Plot an Optimization During Execution" * "Local vs. Global Optima" * "Optimizing a Simulation or Ordinary Differential Equation"* "Optimization App" * "Nonlinear algorithms and examples"* "Unconstrained Nonlinear Optimization Algorithms" * "fminsearch Algorithm"* "fminunc Unconstrained Minimization"* "Minimization with Gradient and Hessian" * "Minimization with Gradient and Hessian Sparsity Pattern" * "Constrained Nonlinear Optimization Algorithms" * "Nonlinear Inequality Constraints" * "Nonlinear Constraints with Gradients" * "fmincon Interior-Point Algorithm with Analytic Hessian"* "Linear or Quadratic Objective with Quadratic Constraints" * "Nonlinear Equality and Inequality Constraints"* "Optimization App with the fmincon Solver" * "Minimization with Bound Constraints and Banded Preconditioner"* "Minimization with Linear Equality Constraints"* "Minimization with Dense Structured Hessian, Linear Equalities"* "One-Dimensional Semi-Infinite Constraints" * "Two-Dimensional Semi-Infinite Constraint"

Author : Perez C.
Publisher :
Page : 328 pages
File Size : 47,97 MB
Release : 2017-08-16
Category :
ISBN : 9781974588053

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In the simplest case, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations comprises a large area of applied mathematics. More generally, 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.MATLAB Optimization Toolbox provides functions for finding parameters that minimize or maximize objectives while satisfying constraints. The toolbox includes solvers for linear programming, mixed-integer linear programming, quadratic programming, nonlinear optimization, and nonlinear least squares. You can use these solvers to find optimal solutions to continuous and discrete problems, perform tradeoff analyses, and incorporate optimization methods into algorithms and applications.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.Also MATLAB Optimization Toolbox provides functions for MULTIOBJECTIVE, QUADRATIC and MIXED DATA PROGRAMMING

Author : Perez C.
Publisher :
Page : 278 pages
File Size : 50,95 MB
Release : 2017-08-16
Category :
ISBN : 9781974587209

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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 : Roy H. Kwon
Publisher : CRC Press
Page : 356 pages
File Size : 50,76 MB
Release : 2013-09-05
Category : Business & Economics
ISBN : 1482204347

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Filling the need for an introductory book on linear programming that discusses the important ways to mitigate parameter uncertainty, Introduction to Linear Optimization and Extensions with MATLAB provides a concrete and intuitive yet rigorous introduction to modern linear optimization. In addition to fundamental topics, the book discusses current l

Author : Amir Beck
Publisher : SIAM
Page : 286 pages
File Size : 31,16 MB
Release : 2014-10-27
Category : Mathematics
ISBN : 1611973643

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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.

Author : Amir Beck
Publisher : SIAM
Page : 364 pages
File Size : 32,51 MB
Release : 2023-06-29
Category : Mathematics
ISBN : 1611977622

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Built on the framework of the successful first edition, this book serves as a modern introduction to the field of optimization. The author’s objective is to provide the foundations of theory and algorithms of nonlinear optimization as well as to present a variety of applications from diverse areas of applied sciences. Introduction to Nonlinear Optimization gradually yet rigorously builds connections between theory, algorithms, applications, and actual implementation. The book contains several topics not typically included in optimization books, such as optimality conditions in sparsity constrained optimization, hidden convexity, and total least squares. Readers will discover a wide array of applications such as circle fitting, Chebyshev center, the Fermat–Weber problem, denoising, clustering, total least squares, and orthogonal regression. These applications are studied both theoretically and algorithmically, illustrating concepts such as duality. Python and MATLAB programs are used to show how the theory can be implemented. The extremely popular CVX toolbox (MATLAB) and CVXPY module (Python) are described and used. More than 250 theoretical, algorithmic, and numerical exercises enhance the reader's understanding of the topics. (More than 70 of the exercises provide detailed solutions, and many others are provided with final answers.) The theoretical and algorithmic topics are illustrated by Python and MATLAB examples. This book is intended for graduate or advanced undergraduate students in mathematics, computer science, electrical engineering, and potentially other engineering disciplines.

Author : Abdelkhalak El Hami
Publisher : John Wiley & Sons
Page : 288 pages
File Size : 25,73 MB
Release : 2021-04-08
Category : Technology & Engineering
ISBN : 1119818257

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This book is a general presentation of complex systems, examined from the point of view of management. There is no standard formula to govern such systems, nor to effectively understand and respond to them. The interdisciplinary theory of self-organization is teeming with examples of living systems that can reorganize at a higher level of complexity when confronted with an external challenge of a certain magnitude. Modern businesses, considered as complex systems, ideally know how to flexibly and resiliently adapt to their environment, and also how to prepare for change via self-organization. Understanding sources of potential crisis is essential for leaders, though not all crises are necessarily bad news, as creative firms know how to respond to challenges through innovation: new products and markets, organizational learning for collective intelligence, and more.

Author : Dingyü Xue
Publisher : Walter de Gruyter GmbH & Co KG
Page : 342 pages
File Size : 42,44 MB
Release : 2020-04-06
Category : Computers
ISBN : 3110667010

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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 : J Lopez
Publisher :
Page : 442 pages
File Size : 20,53 MB
Release : 2019-07-21
Category :
ISBN : 9781080303083

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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. This book develops the functions of Matlab for optimization through examples

Author : William P. Fox
Publisher : CRC Press
Page : 417 pages
File Size : 22,26 MB
Release : 2020-12-08
Category : Mathematics
ISBN : 1000196925

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Optimization is the act of obtaining the "best" result under given circumstances. In design, construction, and maintenance of any engineering system, engineers must make technological and managerial decisions to minimize either the effort or cost required or to maximize benefits. There is no single method available for solving all optimization problems efficiently. Several optimization methods have been developed for different types of problems. The optimum-seeking methods are mathematical programming techniques (specifically, nonlinear programming techniques). Nonlinear Optimization: Models and Applications presents the concepts in several ways to foster understanding. Geometric interpretation: is used to re-enforce the concepts and to foster understanding of the mathematical procedures. The student sees that many problems can be analyzed, and approximate solutions found before analytical solutions techniques are applied. Numerical approximations: early on, the student is exposed to numerical techniques. These numerical procedures are algorithmic and iterative. Worksheets are provided in Excel, MATLAB®, and MapleTM to facilitate the procedure. Algorithms: all algorithms are provided with a step-by-step format. Examples follow the summary to illustrate its use and application. Nonlinear Optimization: Models and Applications: Emphasizes process and interpretation throughout Presents a general classification of optimization problems Addresses situations that lead to models illustrating many types of optimization problems Emphasizes model formulations Addresses a special class of problems that can be solved using only elementary calculus Emphasizes model solution and model sensitivity analysis About the author: William P. Fox is an emeritus professor in the Department of Defense Analysis at the Naval Postgraduate School. He received his Ph.D. at Clemson University and has taught at the United States Military Academy and at Francis Marion University where he was the chair of mathematics. He has written many publications, including over 20 books and over 150 journal articles. Currently, he is an adjunct professor in the Department of Mathematics at the College of William and Mary. He is the emeritus director of both the High School Mathematical Contest in Modeling and the Mathematical Contest in Modeling.