Quasidifferential Calculus (Translations Series in Mathematics and Engineering)

TABLE OF CONTENTS......Page 8
PREFACE......Page 10
1 PRELIMINARIES......Page 14
2 ELEMENTS OF THE THEORYOF MULTIVALUED MAPPINGS......Page 19
3 DIRECTIONAL DERIVATIVES......Page 32
4 CONVEX FUNCTIONS......Page 50
5 SUBLINEAR FUNCTIONS......Page 59
6 THE SPACE OF CONVEX SETS......Page 78
7 UPPER -SEMICONTINUO USLYDIRECTIONALLY DIFFERENTIABLEFUNCTIONS......Page 91
8 THE CLARKS DERIVATIVES......Page 104
9 UPPER CONVEX ANDLOWER CONCAVE APPROXIMATIONS......Page 117
10 Q UASIDIFFERENTIABLE FUNCTIONS......Page 125
11 EXAMPLES......Page 135
12 QUASIDIFFERENTL4BILITY OF A COMPOSITION......Page 141
13 A RELATION BETWEENTHE CLARKE SUBDIFFERENTIALAND THE QUASIDIFFERENTIALS......Page 156
14 IMPLICIT AND INVERSEFUNCTION THEOREMS......Page 168
15 CONES OF ADMISSIBLE DIRECTIONSAND A NONDEGENERACY CONDITION......Page 189
16 NECESSARY AND SUFFICIENTCONDITIONS FOR AN EXTREMUM......Page 201
17 RATE AND DIRECTIONS OFSTEEPEST DESCENT AND ASCENT......Page 216
18 SADDLE POINTS OFQ UASIDIFFERENTIABLE FUNCTIONS......Page 242
19 STAR-SHAPED SETS AND THEIR APPLICATIONSIN NONSMOOTH OPTIMIZATION......Page 249
20 APPROXIMATE Q UASIDIFFERENTIABILITY......Page 267
BIBLIOGRAPHIC NOTES......Page 278
REFERENCES......Page 282
INDEX......Page 296
TRANSLITERATION TABLE......Page 302