Course contents:

Formulation of Optimization Problems in Engineering

Linear Algebra:

Introduction to vector spaces and matrix algebra. Geometric concepts. Unconstrained optimization: Derivation of necessary and sufficiency condition for local optimum Multivariate Unconstrained Optimization -, Line search and trust region methods, Steepest descent, Conjugate gradient, Newton and quasi-Newton methods.

Multivariate Constrained Optimization:

Karush-Kuhn-Tucker conditions for local optimality

Linear Programming:

Simplex, Duality

Quadratic programming:

Active set method

Nonlinear programming:

Penalty function methods, SQP (Successive quadratic programming) Least squares