Optimization from Fundamentals Course | IIT Bombay | Prof. Ankur Kulkarni
Course Details
| Exam Registration | 111 |
|---|---|
| Course Status | Ongoing |
| Course Type | Core |
| Language | English |
| Duration | 12 weeks |
| Categories | Mechanical Engineering, Computational Engineering, Computational Mechanics, Computational Thermo Fluids |
| 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 |
Master the Mathematical Engine of Modern Engineering: Optimization from Fundamentals
In the realms of Mechanical Engineering, Computational Mechanics, and Thermo-Fluids, the ability to find the best possible solution—be it minimizing weight, maximizing efficiency, or optimizing fluid flow—is paramount. This pursuit is governed by the powerful discipline of mathematical optimization. For postgraduate students and professionals seeking to build an unshakable foundation in this critical field, a new comprehensive course, "Optimization from Fundamentals," offers a unique opportunity to learn from a leading expert at India's premier institute.
Your Guide: Prof. Ankur A. Kulkarni, IIT Bombay
This 12-week journey is led by Prof. Ankur A. Kulkarni, Associate Professor and Kelkar Family Chair in Quantitative Finance at IIT Bombay. Prof. Kulkarni is not just an academic theorist; he is a systems theorist whose work bridges the gap between advanced mathematics and real-world, high-stakes applications.
His expertise spans game theory, information theory, control theory, and machine learning, with a focus on strategic inference, privacy, and nudging. His significant consulting roles for major financial regulators like SEBI and institutions like HDFC Life and Kotak Mahindra Bank underscore his ability to apply optimization principles to solve complex problems in algorithmic trading, anti-money laundering, and incentive design. With a Ph.D. from UIUC and recognition from the Indian Academy of Sciences, Prof. Kulkarni brings both deep theoretical knowledge and practical insight to this course.
Who Should Take This Course?
This course is meticulously designed for postgraduate students and professionals in:
- Mechanical Engineering
- Computational Engineering & Computational Mechanics
- Computational Thermo-Fluids
- Mathematics and other Engineering & Science disciplines
Whether you are aiming to enhance your research, tackle complex design problems, or build a robust understanding for advanced simulations, this course provides the essential toolkit.
Course Overview: Building from the Ground Up
True to its title, "Optimization from Fundamentals" does not assume prior expertise. It constructs your knowledge systematically:
- Weeks 1-4: The Foundation. The course begins with an overview of real analysis and convexity, establishing the mathematical language of optimization. You'll then delve into optimization over different domains (open sets, surfaces) and learn the crucial skill of problem transformation.
- Weeks 5-7: Linear Programming (LP). You'll master the workhorse of optimization—Linear Programming. This section covers the simplex method, LP formulation, and the powerful concept of duality, which provides deep economic and sensitivity insights into any LP problem.
- Weeks 8-9: Nonlinear and Convex Optimization. The course then advances to more general problems. You'll learn to identify and solve convex optimization problems, a class where local optima are global, making them tractable and extremely useful in engineering applications.
- Weeks 10-11: Algorithms. Theory meets computation. This module focuses on the iterative methods that power optimization software, exploring algorithms for both linear and nonlinear problems.
- Week 12: Dynamic Optimization. The course culminates with dynamic optimization, which deals with making optimal decisions over time—a key framework in control theory and strategic planning.
Detailed 12-Week Course Layout
| Week | Topic |
|---|---|
| Week 1 | Introduction to optimization and overview of real analysis |
| Week 2 | Optimization over open sets |
| Week 3 | Optimization over surfaces |
| Week 4 | Transformation of optimization problems and convex analysis |
| Week 5 | Introduction to linear programming |
| Week 6 | Linear programming and duality |
| Week 7 | Linear programming and duality (contd.) |
| Week 8 | Nonlinear and convex optimization |
| Week 9 | Nonlinear and convex optimization (contd.) |
| Week 10 | Algorithms |
| Week 11 | Algorithms (contd.) |
| Week 12 | Dynamic optimization |
Why This Course is Essential for Engineers
Optimization is the silent engine behind innovation. For a mechanical engineer, it can mean designing a lighter, stronger chassis. For a computational fluid dynamics specialist, it can mean finding the optimal shape for minimal drag. This course equips you with the fundamental principles to:
- Formulate real-world engineering problems as precise mathematical optimization models.
- Understand the strengths and limitations of different optimization classes (LP, Convex, Nonlinear).
- Interpret results correctly, using concepts like duality for sensitivity analysis.
- Lay the groundwork for using advanced optimization software and libraries effectively.
By learning from Prof. Ankur Kulkarni, you gain not just textbook knowledge, but also an appreciation for how these fundamentals are applied at the highest levels of industry and finance. "Optimization from Fundamentals" is more than a course; it's an investment in a core competency that will define the next generation of engineering solutions.
Enroll Now →