Constrained Optimization and Image Space Analysis. Vol.1: Separation of Sets and Optimality Conditio

Chapter 1. Introduction1.1. Constrained Extremum Problems1.2. Special Extremum Problems1.3. Variational Inequalities, Complernentarity Problems and Generalized Systems1.4. Optimal Design of an Underwater Pipeline1.5. Further Problems in Applied Mechanics1.6. Equilibrium Flows in a Network1.7. Testing Statistical Hypotheses1.8. Vector Problems from Industry1.9. CommentsReferencesChapter 2. Elements of Convex Analysis and Separation2.1. Convex Sets and Cones2.2. Linear Support and Separation2.3. Convex Functions2.4. Some Extensions of Convexity2.5. CommentsReferencesChapter 3. Introduction to Image Space Analysis3.1. Semidifferentiability3.2. Image Problem3.3. Stationarity3.4. Sonic Examples3.5. CommentsReferencesChapter 4. Alternative and Separation4.1. Introduction4.2. Separation Functions4.3. Special Separation Functions4.4. A General Setting for a Theorem of the Alternative4.5. Special Theorems of the Alternative4.6. A Special Separation Theorem4.7. Theorems of the Alternative for Multifunctions4.8. Cone Multifunctions4.9. Systems of Intersection Type4.10. CommentsReferencesChapter 5. Optimality Conditions. Preliminary Results5.1. Introduction5.2. Weak Separation and Sufficient Conditions5.3. Weak Separation and Necessary Conditioim5.4. Sonic Applications5.5. Reciprocal Problems5.6. Connections between Discrete and Continuous Problems5.7 CommentsReferencesGlossary of NotationSubject Index