Optimization - theory and applications

Inhaltsverzeichnis§ 1 Introduction, Examples, Survey.1.1 Optimization problems in elementary geometry.1.2 Calculus of variations.1.3 Approximation problems.1.4 Linear programming.1.5 Optimal Control.1.6 Survey.1.7 Literature.§ 2 Linear Programming.2.1 Definition and interpretation of the dual program.2.2 The FARKAS-Lemma and the Theorem of CARATHEODORY.2.3 The strong duality theorem of linear programming.2.4 An application: relation between inradius and width of a polyhedron.2.5 Literature.§ 3 Convexity in Linear and Normed Linear Spaces.3.1 Separating convex sets in linear spaces.3.2 Separation of convex sets in normed linear spaces.3.3 Convex functions.3.4 Literature.§ 4 Convex Optimization Problems.4.1 Examples of convex optimization problems.4.2 Definition and motivation of the dual program. The weak duality theorem.4.3 Strong duality, KUHN-TUCKER saddle point theorem.4.4 Quadratic programming.4.5 Literature.§ 5 Necessary Optimality Conditions.5.1 GATEAUX and FRECHET Differential.5.2 The Theorem of LYUSTERNIK.5.3 LAGRANGE multipliers. Theorems of KUHN-TUCKER and F. JOHN type.5.4 Necessary optimality conditions of first order in the calculus of variations and in optimal control theory.5.5 Necessary and sufficient optimality conditions of second order.5.6 Literature.§ 6 Existence Theorems for Solutions of Optimization Problems.6.1 Functional analytic existence theorems.6.2 Existence of optimal controls.6.3 Literature.Symbol Index.