Optimization

Optimization [MAL7023] (1 Credit)

Lectures:

• Monday : 11:00- 11:25 AM and 4:30-4:55 PM

• Wednesday : 10:30- 10:55 AM and 4:00-4:25 PM

• Thursday : 11:30- 11:55 AM and 5:00-5:25 PM

• Friday: 10:00- 10:25 AM and 3:30-3:55 PM

Evaluation:

Internal -60 %

• Assignments- 30%

• Quiz- 30%

External-40% (End trimester Examination)

Topics to be covered:

• Linear Programming Problem[4 Lectures]: Linear combination of vectors, Convex set, Convex hull, Linear programming problem, feasible solution, basic feasible solution, graphical solution, Simplex method, Charne’s M method.

• Duality and IPP[6 Lectures]: Dual of an LPP, Integer Programming, Gomory’s cut-constraint method.

• Nonlinear Programming[4 Lectures]: First and second order conditions, Constrained optimization - Lagrange Multipliers, Karush-Kuhn-Tucker conditions.

Books:

• Luenberger, D. G., Linear and Nonlinear Programming, Yinyu Ye, Third Edition, Springer, 2008.

• Kambo, N. S., Mathematical Programming Techniques, Second Edition, Affiliated East West Press, 2005

Course:

• October 15, 2020: Introduction to the Course, Basics of Linear Algebra (revised)
• October 16, 2020: Convex Set, Convex combination, Constraint set and its properties

• October 19, 2020: Simplex Method
• October 21, 2020: Charnes' M Method
• October 22, 2020: Algorithm to write Dual L.P.P
• October 23, 2020: Dual and Primal Relationship

• October 25, 2020: (Quiz-I)

• October 26, 2020: Dual Simplex Method (Assignment-I)
• October 28, 2020: Integer Programming Problem
• October 29, 2020: Gomory's cut constraint Method
• October 30, 2020: Holiday
• October 31, 2020: Non linear programming problem (Quiz-II)

• November 2, 2020: Lagrange's Multiplier Method (Assignment-II)
• November 4, 2020: KKT Conditions
• November 5, 2020: Convex Programming Problems, Global and local Extrema
• November 6, 2020: (Quiz-III)