Cover......Page 1
Title......Page 3
Preface......Page 6
Contents......Page 7
1 Introduction and Problem Formulation......Page 9
2.1 Problem Formulation......Page 15
2.2 Existence Theorems......Page 16
2.3 Set of Minimal Points......Page 26
2.4 Application to Approximation Problems......Page 27
2.5 Application to Optimal Control Problems......Page 31
Exercises......Page 37
3.1 Directional Derivative......Page 39
3.2 Gateaux and Frechet Derivatives......Page 45
3.3 Subdifferential......Page 57
3.4 Quasidifferential......Page 65
3.5 Clarke Derivative......Page 75
Exercises......Page 83
4.1 Definition and Properties......Page 87
4.2 Optimality Conditions......Page 96
4.3 A Lyusternik Theorem......Page 103
Exercises......Page 111
5.1 Problem Formulation......Page 113
5.2 Necessary Optimality Conditions......Page 116
5.3 Sufficient Optimality Conditions......Page 134
5.4 Application to Optimal Control Problems......Page 144
Exercises......Page 164
6.1 Problem Formulation......Page 167
6.2 Duality Theorems......Page 172
6.3 Saddle Point Theorems......Page 176
6.4 Linear Problems......Page 180
6.5 Application to Approximation Problems......Page 183
Exercises......Page 192
7.1 Lowner Ordering Cone and Extensions......Page 195
7.2 Optimality Conditions......Page 210
7.3 Duality......Page 215
Exercises......Page 218
8.1 Linear Quadratic Optimal Control Problems......Page 221
8.2 Time Minimal Control Problems......Page 229
Exercises......Page 246
A Weak Convergence......Page 249
B Reflexivity of Banach Spaces......Page 251
C Hahn-Banach Theorem......Page 253
D Partially Ordered Linear Spaces......Page 257
Bibliography......Page 261
Answers to the Exercises......Page 283
Index......Page 297