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Applied Optimization with MATLAB Programming

Author: Venkataraman, P. Series: Wiley-Interscience series in systems and optimization Publisher: Wiley, 2002.Language: EnglishDescription: 398 p. ; 24 cm.ISBN: 0471349585Type of document: BookBibliography/Index: Includes bibliographical references and index
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Item type Current location Collection Call number Status Date due Barcode Item holds
Book Europe Campus
Main Collection
Print QA402.5 .V46 2002
(Browse shelf)
001156862
Available 001156862
Total holds: 0

Includes bibliographical references and index

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Applied Optimization with Matlab® Programming Contents PREFACE 1 Introduction 1.1 Optimization Fundamentals / 2 1.1.1 Elements of Problem Formulation / 4 1.1.2 Mathematical Modeling / 10 1.1.3 Nature of Solution / 16 1.1.4 Characteristics of the Search Procedure / 20 1.2 In tr oduction to MATLAB / 25 1.2.1 Why MATLAB? / 25 1.2.2 MATLAB Installation Issues / 26 1.2.3 Using MATLAB the First Time / 27 1.2.4 Using the Editor / 33 1.2.5 Creating a Code Snippet / 37 1.2.6 Creating a Program / 40 Problems / 44 2 Graphical Optimization 2.1 Problem Definition / 45 2.1.1 Example 2.1 / 46 2.1.2 Format for the Graphical Display / 47 2.2 Graphical Solution / 48 2.2.1 · MATLAB High-Level Graphics Functions / 48 2.2.2 Example 2.1--Graphical Solution / 50 2.2.3 Displaying the Graphics / 53 2.2.4 Customizing the Figure / 54 2.3 Additional Examples / 56 xiii 1 45 vii Viii CONTENTS 2.3.1 Example 2.2 / 56 2.3.2 Example 2.3 / 64 2.3.3 Example 2.4 / 73 2.4 Additional MATLAB Graphics / 79 2.4.1 Handle Graphics / 80 2.4.2 Graphical User Interface / 81 2.4.3 GUI Code / 84 References / 91 Problems / 92 3 Linear Programming 3.1 Problem Definition / 94 3.1.1 Standard Format / 94 3.1.2 Modeling Issues / 98 3.2 Graphical Solution / 107 3.2.1 Example 3.1 / 110 3.2.2 Characteristics of the Solution / 111 3.2. 3 Different Solution Types / 114 3.3 Numerical Solution--the Simplex Method / 115 3.3.1 Features of the Simplex Method / 115 3.3. 2 Application of Simplex Method / 117 3.3.3 Solution Using MATLAB / 120 3.3.4 Solution Using MATLAB'S Optimization Toolbox / 123 3.4 Additional Examples / 124 3.4.1 Example 3.2--Transportation Problem / 124 3.4.2 Example 3.3--Equality Constraints and Unrestricted Variables / 130 3.4.3 Example 3.4--A Four-Variable Problem / 134 3.5 Additional Topics in Linear Programming / 138 3.5.1 Primal and Dual Problem / 138 3.5.2 Sensitivity Analysis / 148 References / 151 Problems / 152 4 Nonlinear Programming 4.1 Problem Definition / 155 154 93 CONTENTS ÎX 4.1.1 Problem Formulation--Example 4.1 / 155 4.1.2 Discussion of Constraints / 157 4.2 Mathematical Concepts / 159 4.2.1 Symbolic Computation Using MATLAB / 159 4. 2.2 Basic Mathematical Concepts / 162 4.2.3 Taylor's Theorem/Series / 169 4.3 Graphical Solutions / 171 4.3.1 Unconstrained Problem / 171 4.3.2 Equality Constrained Problem / 172 4.3.3 Inequality Constrained Problem / 173 4.3. 4 Equality and Inequality Constraints / 174 4.4 Analytical Conditions / 175 4.4.1 Unconstrained Problem / 176 4.4.2 Equality Constrained Problem / 179 4.4.3 Inequality Constrained Optimization / 186 4.4.4 General Optimization Problem / 191 4.5 Examples / 194 4.5.1 Example 4.2 / 194 4.5.2 Example 4.3 / 196 References / 200 Problems / 201 5 Numerical Techniques--The One-Dimensional Problem 5.1 Problem Definition / 204 5.1.1 Constrained One-Dimensional Problem / 204 5.2 Solution to the Problem / 205 5.2.1 Graphical Solution / 205 5.2.2 Newton-Raphson Technique / 206 5.2.3 Bisection Technique / 209 5.2.4 Polynomial Approximation / 211 5.2.5 Golden Section Method / 214 5.3 Importance of the One-Dimensional Problem / 217 5.4 Additional Examples / 219 5.4.1 Example 5.2--Illustration of General Golden Section Method / 219 5.4.2 Example 5.3--Two-Point Boundary Value Problem / 220 5.4.3 Example 5.4--Root Finding with Golden Section / 223 203 X CONTENTS References / 225 Problems / 225 6 Numerical Techniques for Unconstrained Optimization 6.1 Problem Definition / 227 6.1.1 Example 6.1 / 228 6.1.2 Necessary and Sufficient Conditions / 228 6.1.3 Elements of a Numerical Technique / 229 6.2 Numerical Techniques--Nongradient Methods / 230 6.2.1 Random Walk / 230 6.2.2 Pattern Search / 234 6.2.3 Powell's Method / 238 6.3 Numerical Techniques--Gradient-Based Methods / 241 6.3.1 Steepest Descent Method / 241 6.3.2 Conjugate Gradient (Fletcher-Reeves) Method / 244 6.3.3 Davidon-Fletcher-Powell Method / 246 6.3.4 Broydon-Fletcher-Goldfarb-Shanno Method / 249 6.4 Numerical Techniques--Second Order / 251 6.5 Additional Examples / 253 6.5.1 Example 6.2--Rosenbrock Problem / 253 6.5.2 Example 6.3--Three-Dimensional Flow near a Rotating Disk / 255 6.5.3 Example 6.4--Fitting Bezier Parametric Curves / 258 References / 262 Problems / 263 7 Numerical Techniques for Constrained Optimization 7.1 Problem Definition / 266 7.1.1 Problem Formulation--Example 7.1 / 266 7.1.2 Necessary Conditions / 267 7.1.3 Elements of a Numerical Technique / 269 7.2 Indirect Methods for Constrained Optimization / 270 7.2.1 Exterior Penalty Function (EPF) Method / 271 7.2.2 Augmented Lagrange Multiplier (ALM) Method / 276 7.3 Direct Methods for Constrained Optimization / 281 7.3.1 Sequential Linear Programming (SLP) / 284 7.3.2 Sequential Quadratic Programming (SQP) / 289 265 227 CONTENTS Xi 7.3.3 Generalized Reduced Gradient (GRG) Method / 297 7.3.4 Sequential Gradient Restoration Algorithm (SGRA) / 302 7.4 Additional Examples / 307 7.4.1 Example 7.2--Flagpole Problem / 307 7.4.2 Example 7.3--Beam Design / 310 7.4. 3 Example 7.4--Optimal Control / 313 References / 316 Problems / 316 8 Discrete Optimization 8.1 Concepts in Discrete Programming / 320 8.1.1 Problem Relaxation / 321 8.1.2 Discrete Optimal Solution / 322 8.2 Discrete Optimization Techniques / 324 8.2.1 Exhaustive Enumeration / 326 8.2. 2 Branch and Bound / 329 8.2.3 Dynamic Programming / 336 8.3 Additional Examples / 341 8.3.1 Example 8.4--I Beam Design / 341 8. 3.2 Zero--One Integer Programming / 343 References / 348 Problems / 348 9 Global Optimization 9.1 Problem Definition / 351 9.1.1 Global Minimum / 351 9.1.2 Nature of the Solution / 354 9.1.3 Elements of a Numerical Technique / 356 9.2 Numerical Techniques and Additional Examples / 357 9.2.1 Simulated Annealing (SA) / 358 9.2.2 Genetic Algorithm (GA) / 366 References / 377 Problems / 378 10 Optimization Toolbox from MATLAB 10.1 The Optimization Toolbox / 380 379 350 318 XiÎ CONTENTS 10.1.1 Programs / 380 10.1.2 Using Programs / 382 10.1.3 Setting Optimization Parameters / 384 10.2 Examples / 385 10.2.1 Linear Programming / 385 10.2.2 Quadratic Programming / 386 10.2.3 Unconstrained Optimization / 388 10. 2.4 Constrained Optimization / 389 Reference / 391 Index 393

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