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.