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أخواني في الله أحضرت لكم كتاب Introduction to Linear Optimization and Extensions with MATLAB Roy H. Kwon
![كتاب Introduction to Linear Optimization and Extensions with MATLAB M_i_t_13](https://i.servimg.com/u/f61/15/36/74/14/m_i_t_13.jpg) و المحتوى كما يلي :
Contents Preface vii Acknowledgments xi About the Author xiii 1 Linear Programming 1 1.1 Introduction . 1 1.1.1 The Diet Problem 1 1.1.2 Embedded Assumptions . 5 1.2 General Linear Programming Problems 6 1.2.1 Standard Form of a Linear Program 7 1.2.2 Linear Programming Terminology . 8 1.3 More Linear Programming Examples . 10 1.3.1 Converting Minimization Problems with Absolute Value 16 1.3.2 Network Optimization Models . 19 1.3.2.1 Minimum Cost Flow Problem 20 1.3.2.2 Maximum Flow Problem . 23 1.3.3 Solving Linear Programs with MATLAB R . 25 1.4 Exercises . 29 1.5 Computational Project . 36 2 Geometry of Linear Programming 43 2.1 Introduction . 43 2.2 Geometry of the Feasible Set 43 2.2.1 Geometry of Optimal Solutions . 49 2.3 Extreme Points and Basic Feasible Solutions . 52 2.3.1 Generating Basic Feasible Solutions 58 2.3.1.1 Generating Basic Feasible Solutions with MATLAB R 61 2.3.2 Degeneracy 63 2.4 Resolution (Representation) Theorem . 64 2.4.1 Fundamental Theorem of Linear Programming 67 2.5 Exercises 4.9 Exercises . 172 5 Dantzig-Wolfe Decomposition 177 5.1 Introduction . 177 5.2 Decomposition for Block Angular Linear Programs 177 5.3 Master Problem Reformulation . 180 5.4 Restricted Master Problem and the Revised Simplex Method 182 5.5 Dantzig-Wolfe Decomposition . 185 5.5.1 Economic Interpretation . 201 5.5.2 Initialization . 202 5.5.3 Bounds on Optimal Cost 202 5.6 Dantzig-Wolfe MATLAB R Code 205 5.6.1 DantzigWolfeDecomp MATLAB Code . 207 5.7 Exercises . 211 6 Interior Point Methods 217 6.1 Introduction . 217 6.2 Linear Programming Optimality Conditions . 217 6.2.1 Newton-Raphson Method 219 6.3 Primal-Dual Interior Point Strategy 223 6.3.1 Barrier Reformulation 224 6.3.1.1 Newton-Raphson Method for KKT Conditions of the Barrier Problem 225 6.3.2 General Primal-Dual Interior Point Method 227 6.3.2.1 Starting with an Infeasible Interior Point 228 6.3.3 Complexity of General Primal-Dual Interior Path Following Methods 229 6.3.3.1 Polynomial Complexity of Short-Step PathFollowing Methods . 232 6.4 The Predictor-Corrector Variant of the Primal-Dual Interior Point Method 233 6.4.1 Predictor Step 233 6.4.2 Setting the Centering Parameter 234 6.4.3 Corrector and Centering Step 234 6.4.4 Computational Overhead 235 6.4.5 Predictor-Corrector Algorithm . 235 6.4.5.1 Initial Point Generation 236 6.5 Primal-Dual Interior Point Method in MATLAB R 241 6.5.1 MATLAB Code 242 6.6 Exercises . 244 7 Quadratic Programming 249 7.1 Introduction . 249 7.2 QP Model Structure . 249 7.3 QP Application: Financial Optimization 7.4 Solving Quadratic Programs Using MATLAB R . 257 7.4.1 Generating the Efficient Frontier Using MATLAB 258 7.5 Optimality Conditions for Quadratic Programming . 259 7.5.1 Local and Global Optima 260 7.5.2 Unconstrained Quadratic Programs 261 7.5.2.1 Convex Unconstrained Quadratic Programming (Global Optimality) . 265 7.5.3 Convex Optimization 268 7.5.4 Equality-Constrained Quadratic Programs . 269 7.5.4.1 Alternative Solution Methods for EQP . 273 7.5.5 Inequality Constrained Convex Quadratic Programming 274 7.5.6 Predictor-Corrector Algorithm for Convex QP 275 7.6 Exercises . 281 8 Linear Optimization under Uncertainty 287 8.1 Introduction . 287 8.2 Stochastic Programming 288 8.2.1 Stochastic Programming with Recourse 290 8.2.1.1 Two-Stage Stochastic Programming with Recourse 293 8.3 More Stochastic Programming Examples . 297 8.3.1 Solving Two-Stage Stochastic Programs with Recourse 300 8.3.1.1 Dantzig-Wolfe Decomposition for Stochastic Programming 301 8.3.1.2 L-Shaped Method (Constraint Generation) . 301 8.3.1.3 Convergence of the L-Shaped Method 309 8.4 Robust Optimization 310 8.4.1 Constraint-wise Construction of RC: 311 8.5 Exercises . 318 A Linear Algebra Review 323 Bibliography 329 Index 33 #ماتلاب,#متلاب,#Matlab,
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