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GIAN Course on Advances in Mixed Integer Nonlinear Optimization

Room No. 5, Victor Menezes Convention Centre, IIT Bombay
15-25th January, 2024


Many design, planning and decision problems arising in engineering, sciences, finance, and statistics can be mathematically modeled as Mixed-Integer Nonlinear Optimization (MINLO) problems. The last two decades have seen a phenomenal growth in the development of theory, algorithms and computational tools for MINLO. Riding on this growth, MINLO has found many applications, and is being used to solve practical problems in various domains.

The 10-day (about 50 hours) course will start with a gentle introduction to MINLO models and motivating practical applications. The next part of the course covers the branch-and-cut paradigm which is central to solving these problems followed by methods for convex MINLOs and nonconvex MINLOs. Heuristic search, cutting plane techniques, reformulation and presolving methods will be covered. The course concludes with discussions on the future trends of MINLO. Tutorials for practice problems and exercises will be conducted each day. Hands-on computational exercises on modeling and using state-of-the-art software will help participants understand practical ways of solving MINLOs.

Industry practitioners have the option of registering for a shorter module spanning six days (15-20 January). It will focus on introduction to MINLO, modeling, software and methods for convex MINLO.


  • Sven Leyffer, Argonne National Lab, Chicago
  • Pietro Belotti, Politecnico di Milano
  • Ashutosh Mahajan, IEOR, IIT Bombay

Who may benefit

  1. PhD students, postdoctoral researchers, post-graduate students interested in the techniques and applications of integer optimization
  2. Faculty interested in pursuing research and in teaching integer optimization
  3. Practitioners in industry who model and solve optimization problems for their work


  • Introduction to Mixed-Integer Nonlinear Optimization (MINLO)
  • Modeling and software, with hands-on sessions
  • Applications of MINLO
  • Methods for convex MINLO
  • Branch-and-cut with advanced reformulation techniques
  • Global optimization
  • Cutting planes for convex and nonconvex  MINLO
  • Heuristic approaches for MINLO
  • Future trends and challenges in MINLO


Online registration requires two steps. All students and faculty should register through both, the GIAN portal and the IIT Bombay portal. Practitioners and researchers from industry can register directly with IIT Bombay portal alone.

  1. Registration in the GIAN portal
    Click on the Courses Registration/Participant Login link and follow the instructions there to register for the course 191002K01: Advances in Mixed-Integer Nonlinear Optimization.  
  2. Registration in the IIT Bombay portal
    Click on the above link and follow the link to "Login & Register" at the bottom of the page. Students and faculty from other colleges should register for Module 1 (i.e. the full course). Industry practitioners, employees of government agencies and international participants have the option of registering for Module 1 (full course) or Module 2 (first 6 days only).

Registration fee

Affiliation based fee required in the IIT Bombay registration portal is as follows.

Fees (Rs) for the full course (10 days)
Faculty / College Teachers11,800
Government Organization17,700
Overseas / Foreign National1,77,000


Fees (Rs) for the short-course (6 days)
Government Organization10,620
Overseas / Foreign National1,06,200

The above fees includes taxes. It does not include the registration charges required at the GIAN portal above. The fees does not cover travel, food and accommodation.

Venue and Accommodation

All lectures will be conducted in the Victor Menezes Convention Centre, Room Number 5 on the ground floor.

Limited hostel accommodation is available for students on sharing basis (usually two per room). More details will be posted shortly. Campus guest house may have only limited availability during the course. More information about it and other options will be posted soon.


Approximately five contact hours per day are planned 15-20 January (Monday-Saturday), and 22-25 January (Monday-Thursday). No activity is planned for Sunday, 21st. Lectures and tutorials will be spread between 9AM and 5PM on each day.

Contact us

Queries may be emailed to Ashutosh Mahajan ( Phone number: +91 22 25769418.