Constrained vs Unconstrained Optimization | IIT Kharagpur Course Guide
Course Details
| Exam Registration | 36 |
|---|---|
| Course Status | Ongoing |
| Course Type | Core |
| Language | English |
| Duration | 12 weeks |
| Categories | Mathematics |
| Credit Points | 3 |
| Level | Postgraduate |
| Start Date | 19 Jan 2026 |
| End Date | 10 Apr 2026 |
| Enrollment Ends | 02 Feb 2026 |
| Exam Registration Ends | 20 Feb 2026 |
| Exam Date | 26 Apr 2026 IST |
| NCrF Level | 4.5 — 8.0 |
Mastering Mathematical Optimization: A Deep Dive into Constrained and Unconstrained Methods
In the realms of applied mathematics, economics, engineering, and management science, the ability to find the best possible solution—be it maximizing profits, minimizing costs, or optimizing design—is paramount. This is the domain of mathematical optimization. For postgraduate students and professionals seeking to master these powerful techniques, the 12-week course Constrained and Unconstrained Optimization, offered by esteemed professors from IIT Kharagpur, provides a rigorous and systematic foundation.
Course Overview and Instructors
Designed at the postgraduate level, this course delves into the core principles of Operations Research (OR) and mathematical programming. The instruction is led by two distinguished professors from IIT Kharagpur:
- Prof. Adrijit Goswami: A faculty member since 1992, Prof. Goswami holds an M.Sc. and Ph.D. from Jadavpur University. With over 90 research publications, his expertise spans Inventory Control, Production Planning, Supply Chain Management, Data Mining, and Cryptography. He has guided numerous Ph.D. scholars and brings decades of research and teaching experience to the course.
- Prof. Debjani Chakraborty: A Professor in the Department of Mathematics and Associate Dean at IIT Kharagpur, Prof. Chakraborty contributes significant academic and administrative insight, ensuring the course's content is both deep and accessible.
The course is structured to build from fundamental concepts to advanced applications, making it ideal for M.Sc. students or anyone with a Bachelor's degree in Mathematics.
Who Should Take This Course?
This course is specifically tailored for:
- Intended Audience: Postgraduate (PG) and M.Sc. students in Mathematics, Operations Research, Economics, and Engineering.
- Prerequisites: A B.Sc. degree with Mathematics as a core subject.
- Industry Relevance: While academically focused, the techniques taught are invaluable for any industry that utilizes mathematical modeling for decision-making, including logistics, finance, manufacturing, and data science.
Detailed 12-Week Course Layout
The curriculum is meticulously planned to ensure a comprehensive understanding of optimization.
| Week | Topic | Focus Area |
|---|---|---|
| 1-2 | Linear Programming Problem (LPP) | Formulation, graphical method, introduction to artificial variables. |
| 3-4 | Advanced LPP & Sensitivity Analysis | Duality theory, interpreting shadow prices, and post-optimality analysis. |
| 5-6 | Solution Methods & Applications | Revised and Dual simplex methods, real-world case studies and examples. |
| 7-8 | Unconstrained Optimization (Single Variable) | Classical calculus methods, Fibonacci and Golden Section search techniques. |
| 9 | Unconstrained Optimization (Multiple Variables) | Gradient methods, Newton's method, and understanding convexity. |
| 10 | KKT Conditions | The foundational Karush-Kuhn-Tucker conditions for constrained problems. |
| 11-12 | Constrained Optimization | Direct methods (e.g., Transformation, Penalty) and Indirect methods (using Lagrange multipliers). |
Core Concepts: Constrained vs. Unconstrained Optimization
The course title highlights the two main branches of optimization:
- Unconstrained Optimization: Here, the goal is to find the maximum or minimum of a function without any restrictions on the variable values. Weeks 7-9 focus on techniques for these problems, using derivatives and search algorithms.
- Constrained Optimization: Most real-world problems have limits—budgets, resource capacities, physical laws. These are constraints. Weeks 10-12 teach how to solve problems where the solution must lie within a defined feasible region, primarily using the powerful KKT conditions and Lagrange multipliers.
Essential Reference Books
To supplement the lectures, the course recommends several authoritative texts:
- Optimization: Theory and Applications by S. S. Rao
- Operations Research - An Introduction by Hamdy A. Taha
- Nonlinear Multiobjective Optimization by Kaisa Miettinen
- Optimization for Engineering Design: Algorithms and Examples by Kalyanmoy Deb
Why This Course is Essential
Optimization is not just an academic exercise; it is the engine of efficient decision-making. This course from IIT Kharagpur offers a rare blend of theoretical rigor and practical application. By mastering the content—from the simplex method for linear problems to the KKT conditions for complex nonlinear constraints—students equip themselves with a toolkit that is directly applicable to research and high-level industry challenges in supply chain management, financial modeling, machine learning, and engineering design.
For any postgraduate student looking to solidify their expertise in applied mathematics and operations research, this structured journey through the world of constrained and unconstrained optimization is an invaluable investment.
Enroll Now →