B.Tech Mathematics

MA 321                                   Optimization                                   3-0-0-6

Syllabus: Classification and general theory of optimization; Linear programming (LP) - formulation and geometric ideas, simplex and revised simplex methods, duality and sensitivity, transportation, assignment, and integer programming problems; Nonlinear optimization, method of Lagrange multipliers, Karush-Kuhn-Tucker theory, convex optimization; Numerical methods for unconstrained and constrained optimization (gradient method, Newton’s and quasi-Newton methods, penalty and barrier methods).

Texts:

1. S. Bazaraa, J. J. Jarvis and H. D. Sherali, Linear Programming and Network Flows, 4^th Edition, Wiley, 2011.
2. S. Kambo, Mathematical Programming Techniques, Revised Edition, Affiliated East-West Press, 2008.

References:

1. K. P. Chong and S. H. Zak, An Introduction to Optimization, 4^th Edition, Wiley, 2013.
2. S. Bazaraa, H. D. Sherali and C. M. Shetty, Nonlinear Programming: Theory and Algorithms, 3^rd Edition, Wiley, 2013.
3. G. Luenberger and Y. Ye, Linear and Nonlinear Programming, 4^th Edition, Springer, 2016.
4. G. Murty, Linear Programming, Wiley, 1983.
5. Gale, The Theory of Linear Economic Models, The University of Chicago Press, 1989.