First Year PG Course
The Course Covers: 

Quadratic forms, Hession matrix, definiteness, basic notions of convex analysis, unconstrained

nonlinear optimization, nonlinear programming problems with equality constants, method of

Lagrange multipliers, nonlinear programming problems with inequality contrasts, Kuhn Tucker


Variational calculus, functional, basic variational problem, Euler-Lagrange equation, different

cases of Euler-Lagrange equations constrained variational problem, necessary and sufficient

optimality conditions, functionals depending on higher derivatives, optimal control, optimal

control system with Lagrangian formalism.