# MTH633: Advanced Convex Analysis

Convex sets, convex hull, their properties, separation theorems, hyperplane, Best approximation theorem and its applications, Farkas and Gordan Theorems, Extreme points and Polyhedral. Convex functions, Basic Definitions, properties, various generalizations, differentiable convex functions, subgradient, characterization and applications in linear and nonlinear optimization, complementarity problems and its equivalent formulations.

## Recommended books:

- Convex Analysis by R. Tyrrell Rockafellar.
- Convex Analysis By Jan van Tiel.
- Analysis: Convex Analysis and approximation theoryby R. V. Gamkrelidze, Sergeĭ Mikhaĭlovich Nikolskiĭ.
- Abstract convex Analysis by Ivan Singer.

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