Outline:
Unimodal and Convex functions, Hessian Matrix, Positive definite and Negative definite matrices - One dimensional optimization - Newton's Method- Fibonacci Method- Golden Section Method - Quadratic Interpolation Method.
Multi-dimensional unconstrained optimization - Univariate Method - Neider and Meads Method, Conjugate Directions and Conjugate Gradient – Fletcher-Reeves Method – Davidson-Fletcher- Powell Method.
Multi dimensional constrained optimization - Lagrange multiplier method - Kuhn-Tucker Conditions - Modified Hookes and Jeeves Method - Interior and Exterior Penalty Function Method.
Quadratic Programming – Wolfe’s Method - Beales Method - Geometric Programming Polynomials - Calculus Method - Arithmetic Geometric Inequality Method.
Separable programming - Piecewise linear Approximation Method - Case studies in Non linear Programming.
Books:
1. S.S. Rao, "Optimization: Theory and Applications" 2nd Edition, Wiley Eastern
2. Bazaara, Shetty and Sherali "Non-linear Programming: Theory and Algorithms", Wiley
