# 2K6 EC 805 (F): OPTIMIZATION TECHNIQUES

**Module I: Linear programming I (13 hours)**

Systems of linear equations and inequalities – convex sets – convex functions – formulation of linear programming problems – theory of simplex method – simplex algorithm – Charne’s M method – two phase method – duality in linear programming – dual simplex method**Module II: Linear programming II (13 hours)**

Sensitivity analysis – parametric programming – bounded variable problems – transportation problem – development of the method – integrality property – degeneracy – unbalanced problems – assignment problem – development of the Hungarian method – routing problems**Module III: Nonlinear programming (13 hours)**

Mathematical preliminaries of non-linear programming – gradient and Hessian – unimodal functions – convex and concave functions – role of convexity – unconstrained optimization – fibonacci search – golden section search – optimal gradient method – classical optimization – Lagrange multiplier method – Kuhn-tucker conditions – quadratic programming – separable convex programming – frank and wolfe method**Module IV: Dynamic programming & game theory (13 hours)**

Nature of dynamic programming problem – Bellman’s optimality principle – cargo loading problem – replacement problems – multistage production planning and allocation problems – rectangular games – two person zero sum games – pure and mixed strategies – 2m and m2 games – relation between theory of games and linear programming

**REFERENCES**

1. Bazarra M.S., Jarvis J.J. & Sherali H.D. ‘Linear Programming and Network Problems’, John Wiley

2. Bazarra M.S., Sherali H.D. & Shetty C.M., ‘Nonlinear Programming, Theory and Algorithms’, John Wiley

3. Hadley G., ‘Linear Programming’, Addison Wesley, Narosa

4. Hillier F.S. & Lieberman G.J. ‘Introduction to Operations Research’, McGraw Hill

5. Ravindran A., Phillips D.T. & Solberg J. J., Operations Research Principles and Practice, John Wiley

6. Taha H.A., Operations Research, An introduction, P.H.I.

7. Wagner H.M., ‘Principles of Operations Research with Application to Managerial Decisions’, P.H.I