VARIATIONAL ANALYSIS AND GENERALIZED DIFFERENTIATION: BASIC THEORY

By ABIGAIL HERNANDEZ

CONTENTS VOLUME I BASIC THEORY GENERALIZED DI?ERENTIATION IN BANACH SPACES GENERALIZED NORMALS TO NONCONVEX SETS BASIC DE?NITIONS AND SOME PROPERTIES TANGENTIAL APPROXIMATIONS CALCULUS OF GENERALIZED NORMALS SEQUENTIAL NORMAL COMPACTNESS OF SETS VARIATIONAL DESCRIPTIONS AND MINIMALITY CODERIVATIVES OF SET-VALUED MAPPINGS BASIC DE?NITIONS AND REPRESENTATIONS LIPSCHITZIAN PROPERTIES METRIC REGULARITY AND COVERING CALCULUS OF CODERIVATIVES IN BANACH SPACES SEQUENTIAL NORMAL COMPACTNESS OF MAPPINGS SUBDI?ERENTIALS OF NONSMOOTH FUNCTIONS BASIC DE?NITIONS AND RELATIONSHIPS FR´ECHET-LIKE ?-SUBGRADIENTS AND LIMITING REPRESENTATIONS SUBDI?ERENTIATION OF DISTANCE FUNCTIONS SUBDI?ERENTIAL CALCULUS IN BANACH SPACES SECOND-ORDER SUBDI?ERENTIALS COMMENTARY TO CHAP 1 EXTREMAL PRINCIPLE IN VARIATIONAL ANALYSIS SET EXTREMALITY AND NONCONVEX SEPARATION EXTREMAL SYSTEMS OF SETS VERSIONS OF THE EXTREMAL PRINCIPLE AND SUPPORTING PROPERTIES EXTREMAL PRINCIPLE IN FINITE DIMENSIONS EXTREMAL PRINCIPLE IN ASPLUND SPACES APPROXIMATE EXTREMAL PRINCIPLE IN SMOOTH BANACH SPACES SEPARABLE REDUCTION EXTREMAL CHARACTERIZATIONS OF ASPLUND SPACES RELATIONS WITH VARIATIONAL PRINCIPLES EKELAND VARIATIONAL PRINCIPLE SUBDI?ERENTIAL VARIATIONAL PRINCIPLES SMOOTH VARIATIONAL PRINCIPLES REPRESENTATIONS AND CHARACTERIZATIONS IN ASPLUND SPACES SUBGRADIENTS, NORMALS, AND CODERIVATIVES IN ASPLUND SPACES REPRESENTATIONS OF SINGULAR SUBGRADIENTS AND HORIZONTAL NORMALS TO GRAPHS AND EPIGRAPHS VERSIONS OF EXTREMAL PRINCIPLE IN BANACH SPACES AXIOMATIC NORMAL AND SUBDI?ERENTIAL STRUCTURES SPECI?C NORMAL AND SUBDI?ERENTIAL STRUCTURES ABSTRACT VERSIONS OF EXTREMAL PRINCIPLE COMMENTARY TO CHAP 2 FULL CALCULUS IN ASPLUND SPACES CALCULUS RULES FOR NORMALS AND CODERIVATIVES CALCULUS OF NORMAL CONES CALCULUS OF CODERIVATIVES STRICTLY LIPSCHITZIAN BEHAVIOR AND CODERIVATIVE SCALARIZATION SUBDI?ERENTIAL CALCULUS AND RELATED TOPICS CALCULUS RULES FOR BASIC AND SINGULAR SUBGRADIENTS APPROXIMATE MEAN VALUE THEOREM WITH SOME APPLICATIONS CONNECTIONS WITH OTHER SUBDI?ERENTIALS GRAPHICAL REGULARITY OF LIPSCHITZIAN MAPPINGS SECOND-ORDER SUBDI?ERENTIAL CALCULUS SNC CALCULUS FOR SETS AND MAPPINGS SEQUENTIAL NORMAL COMPACTNESS OF SET INTERSECTIONS AND INVERSE IMAGES SEQUENTIAL NORMAL COMPACTNESS FOR SUMS AND RELATED OPERATIONS WITH MAPS SEQUENTIAL NORMAL COMPACTNESS FOR COMPOSITIONS OF MAPS COMMENTARY TO CHAP 3 CHARACTERIZATIONS OF WELL-POSEDNESS AND SENSITIVITY ANALYSIS NEIGHBORHOOD CRITERIA AND EXACT BOUNDS NEIGHBORHOOD CHARACTERIZATIONS OF COVERING NEIGHBORHOOD CHARACTERIZATIONS OF METRIC REGULARITY AND LIPSCHITZIAN BEHAVIOR POINTBASED CHARACTERIZATIONS LIPSCHITZIAN PROPERTIES VIA NORMAL AND MIXED CODERIVATIVES POINTBASED CHARACTERIZATIONS OF COVERING AND METRIC REGULARITY METRIC REGULARITY UNDER PERTURBATIONS SENSITIVITY ANALYSIS FOR CONSTRAINT SYSTEMS CODERIVATIVES OF PARAMETRIC CONSTRAINT SYSTEMS LIPSCHITZIAN STABILITY OF CONSTRAINT SYSTEMS SENSITIVITY ANALYSIS FOR VARIATIONAL SYSTEMS CODERIVATIVES OF PARAMETRIC VARIATIONAL SYSTEMS CODERIVATIVE ANALYSIS OF LIPSCHITZIAN STABILITY LIPSCHITZIAN STABILITY UNDER CANONICAL PERTURBATIONS COMMENTARY TO CHAP 4 REFERENCES