NOTE: Attempt any FIVE questions selecting at least TWO questions from each section.

Section-I (5/9)

The Mathematical Programming Problem

•    Formal statement of the problem

•    Types of maxima, the Weierstrass Theorem and the Local-Global theorem

•    Geometry of the problem

Classical Programming

•    The unconstrained case

•    The method of Lagrange multipliers

•    The interpretation of the Lagrange multipliers

Non-linear Programming

•    The case of no inequality constraints

•    The Kuhn-Tucker conditions

•    The Kuhn-Tucker theorem

•    The interpretation of the Lagrange multipliers

•    Solution algorithms

Linear Programming

•    The Dual problems of linear programming

•    The Lagrangian approach; Existence, Duality and complementary slackness theorems

•    The interpretation of the dual

•    The simplex algorithm



Section-II (4/9)

The Control Problem

•    Formal statement of the problem

•    Some special cases

•    Types of Control

•    The Control problem as one of programming in on infinite dimensional space; The generalized Weierstrass theorem

Calculus of Variations

•    Euler equations

•    Necessary conditions

•    Transversality condition

•    Constraints

Dynamic Programming

•    The principle of optimality and Bellman’s equation

•    Dynamic programming and the calculus of variations

•    Dynamic programming solution of multistage optimization problems

Maximum Principle

•    Co-state variables, The Hamiltonian and the maximum principle

•    The interpretation of the co-state variables

•    The maximum principle and the calculus of variations

•    The maximum principle and dynamic programming

•    Examples