Convex set, Convex functions and its properties in (R^n), Convex programming, Sub-differential, Sub-gradients and its properties, Normal cone, Kuhn-Tucker theory, Lagrange multipliers, Conjugate functions, The Fenchel-duality theorem, Convex duality, Augmented Lagrange multipliers, Proximal operator and its application to convex optimization and its Complexity and rate of convergence, Conjugate method, Bundel methods and cutting plane scheme.

To introduce students to convex analysis and its theories.

To introduce its application to different types of real-world optimisation problems, especially in data science and image processing.

To introduce different types of convex algorithms for non-smooth optimisation problems.

Also, to introduce the rate of convergence and the complexity of the convex optimisation problems.

Students would learn convex analysis and its theories and apply them to different problems arising in different fields.

Amir Beck, First-order Methods in Optimization, SIAM Series

Stephen Boyd, Convex Optimization, Cambridge Press

Yurii Nestrove, Lecture on Convex Optimization, Springer

R. T. Rockafellar and J. B. R. Wets, Variational Analysis, Springer

. R. T. Rockafellar, Convex Analysis, Princeton University Press

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