Advanced Optimization Techniques: Course Contents (MAT- 672)

Optimization Preliminaries:

Review of the theory of maxima, minima (two variables);  positive definite matrices, convexity of regions and functions; quadratic function and Hessian matrix; uniqueness of minimum.

Unconstrained Optimization:

Single search techniques: Bracketing method; Quadratic and cubic interpolation; Fibonacci search; Golden-section.

Gradient , conjugate- gradient and direct- search methods:

Newton ;Steepest descent; Davidon- Fletcher-Powell ( DFP ); Fletcher- Reeves ; Hooke and Jeeves.

Direct Search methods:

Hooke and Jeeves ; pattern search ; Nelder and Mead ; Simplex method

Constrained Optimization:

Introduction ; review of Lagrange multipliers technique with equality constraints; inequality constraints and slack variables; Kuhn-Tucker

Constrained Optimization ( Contd):

Cutting plane method; Rosen’s projection method.

Sequential linear programming (SLP) and Sequential quadratic programming (SQP) techniques

Interior and Exterior Penalty-functions  to handle equality ,inequality and mixed type of constraints.

Introduction to Calculus of Variations:

Preliminaries; derivation of Euler’s equation with