Contents:Front Cover; Theory of Extremal Problems; Copyright Page; CONTENTS; Preface; Basic notation; CHAPTER 0 INTRODUCTION. BACKGROUND MATERIAL; 0.1 Functional analysis; 0.2 Differential calculus; 0.3 Convex analysis; 0.4 Differential equations; CHAPTER 1 NECESSARY CONDITIONS FOR AN EXTREMUM; 1.1 Statements of the problems and formulations of basic theorems; 1.2 Smooth problems. The Lagrange multiplier rule; 1.3 Convex problems. Proof of the Kuhn-Tucker theorem; 1.4 Mixed problems. Proof of the extremal principle
CHAPTER 2 NECESSARY CONDITIONS FOR AN EXTREMUM IN THE CLASSICAL PROBLEMS OF THE CALCULUS OF VARIATIONS AND OPTIMAL CONTROL2.1 Statements of the problems; 2.2 Elementary derivation of necessary conditions for an extremum in simplest problems of the classical calculus of variations; 2.3 The Lagrange problem. The Euler-Lagrange equation; 2.4 The Pontrjagin maximum principle. Formulation and discussion; 2.5 Proof of the maximum principle; CHAPTER 3 ELEMENTS OF CONVEX ANALYSIS; 3.1 Convex sets and separation theorems; 3.2 Convex functions; 3.3 Conjugate functions. The Fenche1-Moreau theorem
3.4 Duality theorems3.5 Convex analysis in finite-dimensional spaces; CHAPTER 4 LOCAL CONVEX ANALYSIS; 4.1 Homogeneous functions and directional derivatives; 4.2 Subdifferentials. Basic theorems; 4.3 Cones of supporting functionals; 4.4 Locally convex functions; 4.5 The subdifferentials of certain functions; CHAPTER 5 LOCALLY CONVEX PROBLEMS AND THE MAXIMUM PRINCIPLE FOR PROBLEMS WITH PHASE CONSTRAINTS; 5.1 Locally convex problems; 5.2 Optimal control problems with phase constraints; 5.3 Proof of the maximum principle for problems with phase constraints; CHAPTER 6 SPECIAL PROBLEMS
6.1 Linear programming6.2 The theory of quadratic forms in Hilbert space; 6.3 Quadratic functionals in the classical caculus of variations; 6.4 Discrete optimal control problems; CHAPTER 7 SUFFICIENT CONDITIONS FOR AN EXTREMUM; 7.1 The perturbation method; 7.2 Smooth problems; 7.3 Convex problems; 7.4 Sufficient conditions for an extremum in the classical calculus of variations; CHAPTER 8 MEASURABLE MULTIMAPPINGS AND CONVEX ANALYSIS OF INTEGRAL FUNCTIONALS; 8.1 Multimappings and measurability; 8.2 Integration of multimappings; 8.3 Integral functionals
CHAPTER 9 EXISTENCE OF SOLUTIONS IN PROBLEMS OF THE CALCULUS OF VARIATIONS AND OPTIMAL CONTROL9.1 Semicontinuity of the functionals in the calculus of variations and the compactness of their level sets; 9.2 Theorems on the existence of solutions; 9.3 The convolution integral and linear problems; CHAPTER 10 APPLICATION OF THE THEORY TO SPECIFIC PROBLEMS; 10.1 Problems in geometric optics; 10.2 Young's inequality and Helly's theorem; 10.3 Optimal excitation of an oscillator; Problems; Bibliography; Subject Index;