| Introduction. / Chapter 1： |
| Problem Statement and Basic Definitions / 1.1： |
| Illustrative Examples / 1.2： |
| Guidelines for Model Construction / 1.3： |
| Exercises |
| Notes and References |
| Convex Analysis. / Part 1： |
| Convex Sets. / Chapter 2： |
| Convex Hulls / 2.1： |
| Closure and Interior of a Set / 2.2： |
| Weierstrass's Theorem / 2.3： |
| Separation and Support of Sets / 2.4： |
| Convex Cones and Polarity / 2.5： |
| Polyhedral Sets, Extreme Points, and Extreme Directions / 2.6： |
| Linear Programming and the Simplex Method / 2.7： |
| Convex Functions and Generalizations. / Chapter 3： |
| Definitions and Basic Properties / 3.1： |
| Subgradients of Convex Functions / 3.2： |
| Differentiable Convex Functions / 3.3： |
| Minima and Maxima of Convex Functions / 3.4： |
| Generalizations of Convex Functions / 3.5： |
| Optimality Conditions and Duality. / Part 2： |
| The Fritz John and Karush-Kuhn-Tucker Optimality Conditions. / Chapter 4： |
| Unconstrained Problems / 4.1： |
| Problems Having Inequality Constraints / 4.2： |
| Problems Having Inequality and Equality Constraints / 4.3： |
| Second-Order Necessary and Sufficient Optimality Conditions for Constrained Problems / 4.4： |
| Constraint Qualifications. / Chapter 5： |
| Cone of Tangents / 5.1： |
| Other Constraint Qualifications / 5.2： |
| Lagrangian Duality and Saddle Point Optimality Conditions. / 5.3： |
| Lagrangian Dual Problem / 6.1： |
| Duality Theorems and Saddle Point Optimality Conditions / 6.2： |
| Properties of the Dual Function / 6.3： |
| Formulating and Solving the Dual Problem / 6.4： |
| Getting the Primal Solution / 6.5： |
| Linear and Quadratic Programs / 6.6： |
| Algorithms and Their Convergence / Part 3： |
| The Concept of an Algorithm. / Chapter 7： |
| Algorithms and Algorithmic Maps / 7.1： |
| Closed Maps and Convergence / 7.2： |
| Composition of Mappings / 7.3： |
| Comparison Among Algorithms / 7.4： |
| Unconstrained Optimization. / Chapter 8： |
| Line Search Without Using Derivatives / 8.1： |
| Line Search Using Derivatives / 8.2： |
| Some Practical Line Search Methods / 8.3： |
| Closedness of the Line Search Algorithmic Map / 8.4： |
| Multidimensional Search Without Using Derivatives / 8.5： |
| Multidimensional Search Using Derivatives / 8.6： |
| Modification of Newton's Method: Levenberg-Marquardt and Trust Region Methods / 8.7： |
| Methods Using Conjugate Directions: Quasi-Newton and Conjugate Gradient Methods / 8.8： |
| Subgradient Optimization Methods / 8.9： |
| Penalty and Barrier Functions. / Chapter 9： |
| Concept of Penalty Functions / 9.1： |
| Exterior Penalty Function Methods / 9.2： |
| Exact Absolute Value and Augmented Lagrangian Penalty Methods / 9.3： |
| Barrier Function Methods / 9.4： |
| Polynomial-Time Interior Point Algorithms for Linear Programming Based on a Barrier Function / 9.5： |
| Methods of Feasible Directions. / Chapter 10： |
| Method of Zoutendijk / 10.1： |
| Convergence Analysis of the Method of Zoutendijk / 10.2： |
| Successive Linear Programming Approach / 10.3： |
| Successive Quadratic Programming or Projected Lagrangian Approach / 10.4： |
| Gradient Projection Method of Rosen / 10.5： |
| Reduced Gradient Method of Wolfe and Generalized Reduced Gradient Method / 10.6： |
| Convex-Simplex Method of Zangwill / 10.7： |
| Effective First- and Second-Order Variants of the Reduced Gradient Method / 10.8： |
| Linear Complementary Problem, and Quadratic, Separable, Fractional, and Geometric Programming. / Chapter 11： |
| Linear Complementary Problem / 11.1： |
| Convex and Nonconvex Quadratic Programming: Global Optimization Approaches / 11.2： |
| Separable Programming / 11.3： |
| Linear Fractional Programming / 11.4： |
| Geometric Programming / 11.5： |
| Mathematical Review. / Appendix A： |
| Summary of Convexity, Optimality Conditions, and Duality. / Appendix B： |
| Bibliography. |
| Index |
| Introduction. / Chapter 1： |
| Problem Statement and Basic Definitions / 1.1： |
| Illustrative Examples / 1.2： |
Book
