Convex set, Convex functions and their properties in Hilbert space (R^n), Sub-differential, Sub-gradients and their properties, Normal cone, Monotone operator, Maximal monotone operator and its properties, Conjugate functions, The Fenchel-duality theorem, Resolvent and proximal operator, Zeroes of monotone operator, Sum of monotone, Forward-backwards splitting, Peaceman-Rachford splitting, Douglas-Rachford splitting methods and ADMM in Hilbert Spaces (R^n).

To introduce students to monotone operators and their different splitting methods.

To introduce different types of splitting methods in real-world optimisation problems, especially in data science and image processing.

To introduce different types of algorithms for splitting optimisation problems.

Also, the convergences of the different splitting optimisation problems should be introduced.

Students would learn convex analysis and the splitting technique, which will apply the theories to different problems arising in various fields.

. Heinz H. Bauschke and Patrick L. Combette, Convex, Analysis and Monotone Operator Theory in Hilbert Spaces, Springer

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

Stephen Simons, , From Hahn-Banach to Monotonicity, Springer

R Burachik, Set-valued Mappings and Enlargement of Monotone Operators, Springer

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