Programmes → I.M.Sc. in Mathematical Sciences and M.Sc. in Mathematics/Applied Mathematics/Statistics-OR

Non-Linear Programming

Course Code: IM 455; ST 551; MA 486; MM 590; AM 590 | Credits: 4 | Prerequisite: Basic knowledge of Nonlinear Analysis and Linear Algebra

Unit I:(Applications) Introduction to applications of nonlinear programming: optimal control problems, structural design, mechanical design, electrical networks, water resources management, stochastic resource allocation, location of facilities, financial engineering problems.
Unit II:(Optimality Conditions) Nonlinear programming problems, unconstrained problems, problems with inequality and equality constraints, second-order necessary and sufficient optimality conditions for constrained problems (Fritz John and Karush-Kuhn-Tucker conditions).
Unit III:(Convexity and Duality) Review of convex functions and convex optimization; duality and optimality conditions in nonlinear programming.
Unit IV:(Algorithms) Algorithms for solving nonlinear programmes: line search methods, method of feasible directions; focus on a special application in financial engineering, supply chain management, airline optimization or production planning.

Discuss and classify non-linear programming problems.
Solve non-linear programming problems.
Discuss the problems of unconstrained nonlinear programming.
Discuss the necessary and sufficient conditions for the solution of unconstrained problems.
Apply methods for restricted non-linear programming problems.
Discuss approximate solutions of restricted problems.

Bazaraa, Mokhtar S., Jarvis, John J. and Sherali, Hanif D. Linear Programming and Network Flows. 2nd ed. Wiley, 2003
Ravindran, A. Ravi (ed.). Operations Research and Management Science Handbook. CRC Press, 2009
Cottle, Richard W. and Lemke, Carlton E. (eds.). Nonlinear Programming. American Mathematical Society, 1976
Bertsekas, Dimitri P. Nonlinear Programming. Athena Scientific, 1999