Numerical Optimization

Code: MA3221 | L-T-P-C: 3-0-2-8

Optimization Problems, Convex Sets and Convex Functions, Extremum Points.

Unconstrained Optimization:  Search methods: Powell’s Method, Hooke and Jeeves Method; Steepest Descent Method, Fletcher and Reeves Method, Newton’s Method, Marquardt’s Method, Quasi-Newton Methods, Davidson-Fletcher-Powell Method, Least Square Problems.

Constrained Optimization: Lagrange multiplies, Kuhn-Tucker Conditions, Duality, Simplex Method, Dual methods, Active Set Methods for Convex Quadratic Programming, Gradient Projection Methods, Penalty-Barrier Methods.

Texts:

• Jorge Nocedal and Stephen Wright, Numerical Optimization, Second Edition, Springer Verlag, 2006.
• D. P. Bertsekas, Nonlinear Programming, Athena Scientific, 1999.

 

References:

• Suresh Chandra, Jaydeva, Aparna Mehra, Numerical Optimization with Applications, Narosa, 2009.
• S. S. Rao, Optimization: Theory and Applications, Second Edition, Wiley Eastern, 1984
• David Luenberger and Yinyu Ye, Linear and Nonlinear Programming, Fourth Edition, Springer, 2016.
• E. K. P. Chong and S. H. Zak, Introduction to Optimization, Fourth Edition, Wiley India, 2017.
• S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge India, 2016.