Constrained And Unconstrained Optimization

By Prof. Adrijit Goswami, Prof. Debjani Chakraborty   |   IIT Kharagpur
Learners enrolled: 71
About the course:
This course has been designed for postgraduate students. Operations research is not only important in its own right but also forms an integral part of applied sciences like economics, management science, engineering design problems etc. The course provides a systematic and thorough discussion on subject matter with numerous examples.


PREREQUISITES :  B.Sc  with Mathematics as a subject

INDUSTRY SUPPORT :  Purely academic course. The content is helpful for all industries who deal with mathematical programming techniques.
Course Status : Upcoming
Course Type : Core
Duration : 12 weeks
Start Date : 23 Jan 2023
End Date : 14 Apr 2023
Exam Date : 30 Apr 2023 IST
Enrollment Ends : 30 Jan 2023
Category :
  • Mathematics
Credit Points : 3
Level : Postgraduate

Page Visits

Course layout

Week 1: Linear Programming Problem
Week 2: LPP with artificial variable
Week 3: More on LPP & Introduction to sensitivity Analysis
Week 4: Sensitivity and duality
Week 5: Revised and Dual simplex method
Week 6: Discussion on application with examples
Week 7: Unconstrained optimization with single variable
Week 8: Discussion on Elimination techniques
Week 9: Unconstrained optimization with multiple variable
Week 10:KKT conditions
Week 11:Constrained optimization – direct method
Week 12:Constrained optimization – indirect method

Books and references

1. Optimization: Theory and applications By S. S. Rao

2. Operations Research - An Introduction By Hamdy A. Taha

3. Nonlinear Multiobjective Optimization By Kaisa Miettinen


5.  Algorithms and Examples By KALYANMOY DEB

Instructor bio

Prof. Adrijit Goswami

IIT Kharagpur
Adrijit Goswami joined the Institute as a Faculty member in 1992. He received his M.Sc. and Ph.D. degree from Jadavpur University, India in 1985 and 1991 respectively. His research interest and publications have been on Operations Research and Theoretical Computer Science. His initial interest has been in developing mathematical models in Inventory Control under deterministic, probabilistic and fuzzy environment. For the past several years he has been involved in various aspects of database systems, data mining and cryptography and computer network as a researcher. Professor Goswami has guided 14 research scholars in their Ph.D. programs and at present guiding 7 students. He is author and co-author of more than 90 research publications in major International journals in the area of Operations Research and Theoretical Computer Science. He is also member of the editorial board of several International/National research journals. His current interests and publications have been on Production Planning and Control, Supply Chain management, Data Mining, Cryptography, Hierarchial access Control and Network security.

Prof. Debjani Chakraborty

Dr.Debjani Chakraborty is Associate Professor in Department of Mathematics, IIT Kharagpur.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 
30 April 2023 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.


Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Kharagpur .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

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