| Preface | p. xi |
| Introduction | |
| Analysis | |
| Classical Optimization--Unconstrained and Equality Constrained Problems | |
| Unconstrained Extrema | p. 9 |
| Equality Constrained Extrema and the Method of Lagrange | p. 15 |
| Exercises | p. 24 |
| References | p. 25 |
| Optimality Conditions for Constrained Extrema | |
| First Order Necessary Conditions for Inequality Constrained Extrema | p. 28 |
| Second Order Optimality Conditions | p. 45 |
| Saddlepoints of the Lagrangian | p. 51 |
| Exercises | p. 56 |
| References | p. 60 |
| Convex Sets and Functions | |
| Convex Sets | p. 63 |
| Convex Functions | p. 71 |
| Differential Properties of Convex Functions | p. 83 |
| Extrema of Convex Functions | p. 92 |
| Optimality Conditions for Convex Programs | p. 95 |
| Exercises | p. 100 |
| References | p. 103 |
| Duality in Nonlinear Convex Programming | |
| Conjugate Functions | p. 106 |
| Dual Convex Programs | p. 112 |
| Optimality Conditions and Lagrange Multipliers | p. 125 |
| Duality and Optimality for Standard Convex Programs | p. 131 |
| Exercises | p. 139 |
| References | p. 141 |
| Generalized Convexity | |
| Quasiconvex and Pseudoconvex Functions | p. 145 |
| Arcwise Connected Sets and Convex Transformable Functions | p. 160 |
| Local and Global Minima | p. 172 |
| Exercises | p. 178 |
| References | p. 181 |
| Analysis of Selected Nonlinear Programming Problems | |
| Quadratic Programming | p. 185 |
| Stochastic Linear Programming with Separable Recourse Functions | p. 189 |
| Geometric Programming | p. 196 |
| Exercises | p. 209 |
| References | p. 210 |
| Methods | |
| One-Dimensional Optimization | |
| Newton's Method | p. 216 |
| Polynomial Approximation Methods | p. 221 |
| Direct Methods--Fibonacci and Golden Section Techniques | p. 225 |
| Optimal and Golden Block Search Methods | p. 233 |
| Exercises | p. 241 |
| References | p. 242 |
| Multidimensional Unconstrained Optimization without Derivatives: Empirical and Conjugate Direction Methods | |
| The Simplex Method | p. 245 |
| Pattern Search | p. 247 |
| The Rotating Directions Method | p. 249 |
| Conjugate Directions | p. 255 |
| Powell's Method | p. 259 |
| Avoiding Linearly Dependent Search Directions | p. 265 |
| Further Conjugate Direction-Type Algorithms | p. 275 |
| Exercises | p. 281 |
| References | p. 285 |
| Second Derivative, Steepest Descent and Conjugate Gradient Methods | |
| Newton-Type and Steepest Descent Methods | p. 288 |
| Conjugate Gradient Methods | p. 299 |
| Convergence of Conjugate Gradient Algorithms | p. 307 |
| Exercises | p. 316 |
| References | p. 318 |
| Variable Metric Algorithms | |
| A Family of Variable Metric Algorithms | p. 322 |
| Quasi-Newton Methods | p. 341 |
| Variable Metric Algorithms without Derivatives | p. 353 |
| Recent Methods Based on Nonquadratic Functions | p. 355 |
| Exercises | p. 364 |
| References | p. 367 |
| Penalty Function Methods | |
| Exterior Penalty Functions | p. 372 |
| Interior Penalty Functions | p. 378 |
| Parameter-Free Penalty Methods | p. 385 |
| Exact Penalty Functions | p. 388 |
| Multiplier and Lagrangian Methods | p. 399 |
| Some Computational Aspects of Penalty Function Methods | p. 410 |
| Exercises | p. 412 |
| References | p. 415 |
| Solution of Constrained Problems by Extensions of Unconstrained Optimization Techniques | |
| Extensions of Empirical Methods | p. 420 |
| Gradient Projection Algorithms for Linear Constraints | p. 423 |
| A Quadratic Programming Algorithm | p. 437 |
| Feasible Direction Methods | p. 442 |
| Projection and Feasible Direction Methods for Nonlinear Constraints | p. 449 |
| Exercises | p. 454 |
| References | p. 457 |
| Approximation-Type Algorithms | |
| Methods of Approximation Programming | p. 461 |
| Reduced-Gradient Algorithms | p. 469 |
| Cutting Plane Methods | p. 477 |
| Complementary Convex Programming | p. 483 |
| Exercises | p. 494 |
| References | p. 496 |
| Author Index | p. 499 |
| Subject Index | p. 504 |
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