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
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