EP8199 - Global Optimization of Mixed-Integer and Non-Convex Problems


New from the academic year 2022/2023

Examination arrangement

Examination arrangement: Assignment
Grade: Passed / Not Passed

Evaluation Weighting Duration Grade deviation Examination aids
Assignment 100/100

Course content

The course presents the theory and practice of deterministic algorithms for locating the global solution of NP-hard optimization problems. Recurring themes and methods are convex relaxations, branch-and-bound, cutting planes, outer approximation and primal-dual approaches. Emphasis is placed on the connection between methods. As the course progresses, these methods will be applied and illustrated in the development of algorithms for mixed-integer linear programs, mixed-integer convex programs, nonconvex programs, and mixed-integer nonconvex programs. The broad range of engineering applications for these optimization formulations will also be emphasized.

Learning outcome


The course provides a presentation of the following topics:

  • Introduction to the different classes of optimization (Linear Programming - LP, Mixed-Integer Linear Programming - MILP, Convex Nonlinear Programming, Mixed-Integer Convex Programming - MICP, Nonconvex Nonlinear Programming - NLP, and Nonconvex Mixed-Integer Programming - MINLP
  • Motivation for Global Optimization
  • Background concepts: Convex Optimization, Optimality Criteria for NLPs, Duality Theory and Computational Complexity
  • Attaining Global Information: Interval Analysis, Convex and Concave Relaxations
  • MILPs - Problem formulation and Branch-and Bound based solution algorithms
  • NLPs - Solution using spatial Branch-and-Bound algorithms
  • MICPs - Solution using Outer Approximation and Generalized Benders Decomposition
  • MINLPs - Solution using Branch-and-Bound based algorithms, Nonconvex Generalized Benders Decomposition and Nonconvex Outer Approximation


  • Have an understanding of how to formulate and solve optimization problems appropriately using commercial software (e.g. JuMP in Julia, or GAMS)
  • Have an overview of the workings behind several state-of-the-art algorithms for various problem classes. Know which algorithms are appropriate for what types of problems

General Competence:

  • Learning how to use computational tools to support decision-making for a variety of engineering problems

Learning methods and activities

A hybrid teaching form will be used, where a considerable degree of Self-learning is combined with Q&A Colloquiums with one or more lecturers and the students of this course. As mentioned below, videos from a similar course at MIT will also be made available together with a text book and a considerable set of slides explaining some of the details of the curriculum. The course will also have assignments with solutions.

Further on evaluation

The exam will take the form of a written report based on a project chosen by the student that s related to the PhD research of the candidate, and where the tools and methods provided in this course are utilized.

The grading of the exam will be pass / no pass, where 70 points (of 100) score is required to pass.

Required previous knowledge


Course materials

  • Paul I. Barton: Mixed-Integer and Nonconvex Optimization, Department of Chemical Engineering, Massachusetts Institute of Technology (MIT), Cambridge, MA 02139, USA, 2011 (Textbook)
  • Paul I. Barton: Videos from lectures at MIT, Spring 2021
  • Set of slides related to details in the textbook

More on the course

Version: 1
Credits:  7.5 SP
Study level: Doctoral degree level


Term no.: 1
Teaching semester:  AUTUMN 2022

Language of instruction: English

Location: Trondheim

Subject area(s)
  • Industrial Process Technology
  • Design Methodology
  • Energy and Process Engineering
Contact information
Course coordinator: Lecturer(s):

Department with academic responsibility
Department of Energy and Process Engineering


Examination arrangement: Assignment

Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
Autumn ORD Assignment 100/100
Room Building Number of candidates
  • * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.

For more information regarding registration for examination and examination procedures, see "Innsida - Exams"

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