This is a topics course, which means that the content covered is different every semester the course is offered. The specific topics to be covered in each offering of the course will be announced along with the names of instructors. Instructors can add a topic after informing IEOR department.
Jan-May 2026 Semester
Course Instructor: Ashutosh Mahajan, amahajan@iitb.ac.in
Topic: Mixed-Integer Nonlinear Optimization
Description: Optimization models with nonlinear functions in constraints or the objective along with integer variables arise in various applications. We will study some examples of Mixed-Integer Nonlinear Optimization (MINLO) applied to some applications and general purpose methods for solving them. Some exposure to modeling and solving tools will also be provided. Here is a tentative list of topics that will be covered:
- Convex MINLOs (LP/NLP based methods, Benders, Branch-and-Bound)
- Broad methods for global optimization of nonconvex MINLOs (Spatial branch-and-cut)
- Presolving and bound tightening
- Heuristics
- Cutting planes
- Automatic reformulation
- Applications like water network design, power flow, portfolio optimization etc.
The course is open to PhD, MTech, MSc students who have already done IE609 or IE716 or IE 647 or equivalent (i.e. a course on nonlinear optimization or integer optimization).
JUL-Nov 2025 Semester
This is the content for the course planned in the July -November Semester 2025:
Advanced topics in Combinatorial Game Theory, with emphasis on excellence in research of individual projects. Prerequisite IE619.
References:
A. N. Siegel, Combinatorial Game Theory, American Math. Society, 2013.
U. Larsson, Lecture Notes in Combinatorial Game Theory, IE619, https://www.ieor.iitb.ac.in/larsson
Contents for the previous course in the July - November 2024 semester are here.
Prerequisites: Instructor's permission
Some contents for the version of this course in earlier semesters
This course would cover many basic topics and few important results in Mathematics related to
Operations research. The majority of the content (at least 60%) would be from ‘A First course in
optimization theory’ by Rangarajan Sundaram and the remaining portion would cover some math
basic tools required for Probability. Broadly it attempts to cover the following
• Analysis Sequences and limits, Open, closed, convex and compact sets, limit superior and limit inferior, Matrices, Continuity and differentiability of functions, Intermediate and mean value theorems, Implicit function theorem.
• Optimization Weierstrass Theorem, Theorem of Lagrange, Convex structures in optimization,
Kuhn and Tucker Theorems Parametric continuity: Maximum theorem
• Probability Monotone class theorem, Integration, and expectation, Some measure-theoretic concepts, some more concepts related to probability theory.
If time permits might cover some important stochastic processes.
The focus of the course could be on recent models, techniques computations, and/or applications.
A selection from the following topics :
* Advanced simulation techniques
* Conic programming
* Interior point methods
* Learning algorithms
* Martingale theory
* Queueing systems
* Stochastic games and stochastic control.
The specific topics to be covered in each offering of the course will be announced along with the instructors. Instructors can add a topic after informing IEOR department.
References
- Vivek S. Borkar, Stochastic approximations: A dynamical system viewpoint, 2008, Hindustan Book Agency, New Delhi TRIM series
- K. Talluri and G. van Ryzin, 2002, The theory and practice of Revenue Management, Kluwer, Amsterdam
- R. L. Phillips, Pricing and Revenue Optimization, 2004, Stanford Univ. Press, Stanford
- James Renegar, A Mathematical View of Interior-point Methods in Convex Optimization, SIAM, 2001
- Ronald Wolff, Stochastic modeling and the theory of qaueues, Prentice-Hall, 1989
- L.C.G. Rogers and D. Williams, Diffusions, Markov processes and martingales, Vols. 1 and 2 John Wiley & Sons, 1994
- Jerry Banks, Handbook of Simulation: Principles, Methodology, Advances, Applications, and Practice, Wiley, 1998.
- Open literature from journals and periodicals that exemplify the recent progress in the field of industrial engineering and operations research.
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