| Preface | p. ix |
| Introduction | p. 1 |
| Optimization view on mathematical models | p. 1 |
| NLP models, black-box versus explicit expression | p. 3 |
| Mathematical modeling, cases | p. 7 |
| Introduction | p. 7 |
| Enclosing a set of points | p. 7 |
| Dynamic decision strategies | p. 10 |
| A black box design; a sugar centrifugal screen | p. 13 |
| Design and factorial or quadratic regression | p. 15 |
| Nonlinear optimization in economic models | p. 17 |
| Spatial economic-ecological model | p. 18 |
| Neoclassical dynamic investment model for cattle ranching | p. 19 |
| Several optima in environmental economics | p. 19 |
| Parameter estimation, model calibration, nonlinear regression | p. 20 |
| Learning of neural nets seen as parameter estimation | p. 24 |
| Summary and discussion points | p. 26 |
| Exercises | p. 27 |
| NLP optimality conditions | p. 31 |
| Intuition with some examples | p. 31 |
| Derivative information | p. 35 |
| Derivatives | p. 36 |
| Directional derivative | p. 36 |
| Gradient | p. 37 |
| Second-order derivative | p. 38 |
| Taylor | p. 40 |
| Quadratic functions | p. 41 |
| Optimality conditions, no binding constraints | p. 45 |
| First-order conditions | p. 45 |
| Second-order conditions | p. 46 |
| Optimality conditions, binding constraints | p. 48 |
| Lagrange multiplier method | p. 49 |
| Karush-Kuhn-Tucker conditons | p. 52 |
| Convexity | p. 54 |
| First-Order conditions are sufficient | p. 56 |
| Local minimum point is global minimum point | p. 57 |
| Maximum point at the boundary of the feasible area | p. 59 |
| Summary and discussion points | p. 60 |
| Exercises | p. 60 |
| Appendix: Solvers for Examples 3.2 and 3.3 | p. 64 |
| Goodness of optimization algorithms | p. 67 |
| Effectiveness and efficiency of algorithms | p. 67 |
| Effectiveness | p. 68 |
| Efficiency | p. 69 |
| Some basic algorithms and their goodness | p. 70 |
| Introduction | p. 70 |
| NLP local optimization: Bisection and Newton | p. 71 |
| Deterministic GO: Grid search, Piyavaskii-Shubert | p. 74 |
| Stochastic GO: PRS, Multistart, Simulated Annealing | p. 78 |
| Investigating algorithms | p. 84 |
| Characteristics | p. 85 |
| Comparison of algorithms | p. 87 |
| Summary and discussion points | p. 88 |
| Exercises | p. 89 |
| Nonlinear Programming algorithms | p. 91 |
| Introduction | p. 91 |
| General NLP problem | p. 91 |
| Algorithms | p. 91 |
| Minimizing functions of one variable | p. 93 |
| Bracketing | p. 93 |
| Bisection | p. 94 |
| Golden Section search | p. 95 |
| Quadratic interpolation | p. 97 |
| Cubic interpolation | p. 99 |
| Method of Newton | p. 100 |
| Algorithms not using derivative information | p. 101 |
| Method of Nelder and Mead | p. 102 |
| Method of Powell | p. 105 |
| Algorithms using derivative information | p. 106 |
| Steepest descent method | p. 107 |
| Newton method | p. 108 |
| Conjugate gradient method | p. 109 |
| Quasi-Newton method | p. 111 |
| Inexact line search | p. 113 |
| Trust region methods | p. 115 |
| Algorithms for nonlinear regression | p. 118 |
| Linear regression methods | p. 118 |
| Gauss-Newton and Levenberg-Marquardt | p. 120 |
| Algorithms for constrained optimization | p. 121 |
| Penalty and barrier function methods | p. 121 |
| Gradient projection method | p. 125 |
| Sequential quadratic programming | p. 130 |
| Summary and discussion points | p. 131 |
| Exercises | p. 132 |
| Deterministic GO algorithms | p. 137 |
| Introduction | p. 137 |
| Deterministic heuristic, DIRECT | p. 138 |
| Selection for refinement | p. 139 |
| Choice for sampling and updating rectangles | p. 141 |
| Algorithm and illustration | p. 142 |
| Stochastic models and response surfaces | p. 144 |
| Mathematical structures | p. 147 |
| Concavity | p. 148 |
| Difference of convex functions, d.c. | p. 149 |
| Lipschitz continuity and bounds on derivatives | p. 150 |
| Quadratic functions | p. 154 |
| Bilinear functions | p. 155 |
| Multiplicative and fractional functions | p. 156 |
| Interval arithmetic | p. 158 |
| Global Optimization branch and bound | p. 159 |
| Examples from nonconvex quadratic programming | p. 161 |
| Example concave quadratic programming | p. 162 |
| Example indefinite quadratic programming | p. 163 |
| Cutting planes | p. 165 |
| Summary and discussion points | p. 168 |
| Exercises | p. 169 |
| Stochastic GO algorithms | p. 171 |
| Introduction | p. 171 |
| Rondom sampling in higher dimensions | p. 172 |
| All volume to the boundary | p. 172 |
| Loneliness in high dimensions | p. 173 |
| PRS- and Multistart-based methods | p. 174 |
| Pure Random Search as benchmark | p. 174 |
| Multistart as benchmark | p. 176 |
| Clustering to save on local searches | p. 178 |
| Tunneling and filled functions | p. 180 |
| Ideal and real, PAS and Hit and Run | p. 183 |
| Population algorithms | p. 187 |
| Controlled Random Search and Raspberries | p. 188 |
| Genetic algorithms | p. 191 |
| Particle swarms | p. 195 |
| Summary and discussion points | p. 197 |
| Exercises | p. 197 |
| References | p. 199 |
| Index | p. 205 |
| Table of Contents provided by Ingram. All Rights Reserved. |
