This book serves as an introductory text to optimization theory in normed spaces and covers all areas of nonlinear optimization. It presents fundamentals with particular emphasis on the application to problems in the calculus of variations, approximation and optimal control theory. The reader is expected to have a basic knowledge of linear functional analysis.

1 Introduction and Problem Formulation.- 2 Existence Theorems for Minimal Points.- 3 Generalized Derivatives.- 4 Tangent Cones.- 5 Generalized Lagrange Multiplier Rule.- 6 Duality.- 7 Direct Treatment of Special Optimization Problems.- A Weak Convergence.- B Reflexivity of Banach Spaces.- C Hahn-Banach Theorem.- D Partially Ordered Linear Spaces.