Syllabus

Concept of space, positive definite matrices, linearity, convex set, convex function Unconstrained optimizations for single and multi-variable problems, Newton step, backtracking line search method Constrained optimization techniques for linear and nonlinear problem, simplex method, active set methods concept of duality, Central path, penalty function, interior point methods Self-Concordant functions and Newton Method Complexity analysis Semidefinite programming, LMI, Evolutionary algorithms, Swarm optimization.

Students will be competent in critical questioning and analysis of the mathematical tools used to develop different optimization methods used in control applications.

At the end of the course, students will be able
(I) To visualize, formulate and analyse an optimization problem.
(II) To apply different solution techniques to solve optimization problems.
(III) To apply optimization techniques to control problems.

S. Boyd and L. Vandenberghe, Convex optimization, Cambridge University Press , 2004

D. P. Bertsekas, Nonlinear programming, Athena Scientific , 2016

D. E. Goldberg, Genetic Algorithms in search, Optimization and Machine Learning, Pearson India , 2002

S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM , 1994