Abstract Convex Analysis

This book examines abstract convex analysis and presents the results of recent research, specifically on parametrizations of Minkowski type dualities and of conjugations of type Lau. It explains the main concepts through cases and detailed proofs.Der Schwerpunkt dieses Buches liegt auf der verallgemeinerten konvexen Analysis, einem speziellen Optimierungsverfahren, dessen Bedeutung für eine Reihe angewandter Disziplinen zunimmt. Zufallsmengen und Funktionen werden diskutiert; Sie finden Ausführungen zu allen neuen Entwicklungen der letzten beiden Jahrzehnte. Abstract Convexity of Elements of a Complete Lattice.

Abstract Convexity of Subsets of a Set.

Abstract Convexity of Functions on a Set.

Abstract Quasi-Convexity of Functions on a Set.

Dualities Between Complete Lattices.

Dualities Between Families of Subsets.

Dualities Between Sets of Functions.

Conjugations.

v-Dualities and _|_-Dualities.

Abstract Subdifferentials.

Notes and Remarks.

References.

Indexes. Aus dem Inhalt:
Introduction;
From Complex Analysis to Abstract Convex Analysis;
Abstract Convexity of Elements of a Complete Lattice;
Abstract Convexity of Subsets of a Set;
Abstract Convexity of Functions on a Set;
Abstract Quasi-Convexity of Functions on a Set;
Dualities between Complete Lattices;
Dualities between Families of Subsets;
Dualities between Sets of Functions;
Conjugations;
V-Dualities and I-Dualities;
Abstract Subdifferentials;
Index.

Ivan Singer is the author of Abstract Convex Analysis, published by Wiley.