Basic Mathematical Programming Theory

Preface -- Chapter 1. Basic Notions and Definitions -- 1.1. Introduction -- 1.2. Basic Notions of Analysis and Linear Algebra -- 1.3. Basic Notions and Properties of Optimization Problems -- Chapter 2. Elements of Convex Analysis. Theorems of the Alternative for Linear Systems. Tangent Cones -- 2.1. Elements of Convex Analysis -- 2.2. Theorems of the Alternative for Linear Systems -- 2.3. Tangent Cones -- Chapter 3. Convex Functions and Generalized Convex Functions -- 3.1. Convex Functions -- 3.2. Generalized Convex Functions -- 3.3. Optimality Properties of Convex and Generalized Convex Functions. Theorems of the Alternative for Nonlinear Systems -- Chapter 4. Unconstrained Optimization Problems. Set-Constrained Optimization Problems. Classical Constrained Optimization Problems -- 4.1. Unconstrained Optimization Problems -- 4.2. Set-Constrained Optimization Problems -- 4.3. Optimization Problems with Equality Constraints (“Classical Constrained Optimization Problems”) -- Chapter 5. Constrained Optimization Problems with Inequality Constraints -- 5.1. First-Order Conditions -- 5.2. Constraint Qualifications -- 5.3. Second-Order Conditions -- 5.4. Other Formulations of the Problem. Some Examples -- Chapter 6. Constrained Optimization Problems with Mixed Constraints -- 6.1. First-Order Conditions -- 6.2. Constraint Qualifications -- 6.3. Second-Order Conditions -- 6.4. Problems with a Set Constraint. Asymptotic Optimality Conditions -- Chapter 7.Sensitivity Analysis -- 7.1. General Results -- 7.2. Sensitivity Results for Right-Hand Side Perturbations -- Chapter 8. Convex Optimization: Saddle Points Characterization and Introduction to Duality -- 8.1. Convex Optimization: Saddle Points Characterization -- 8.2. Introduction to Duality -- Chapter 9. Linear Programming and Quadratic Programming -- 9.1. Linear Programming -- 9.2. Duality for Linear Programming -- 9.3. Quadratic Programming -- Chapter 10. Introduction to Nonsmooth Optimization Problems -- 10.1. The Convex Case -- 10.2. The Lipschitz Case -- 10.3. The Axiomatic Approach of K.-H. Elster and J. Thierfelder to Nonsmooth Optimization -- Chapter 11. Introduction to Multiobjective Optimization -- 11.1. Optimality Notions -- 11.2. The Weighted Sum Method and Optimality Conditions -- References -- Index.