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

New from the academic year 2022/2023

### Examination arrangement

Examination arrangement: Assignment

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

Knowledge:

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

Skills:

• 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.

None

### 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
Facts

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

Coursework

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 of Energy and Process Engineering

# Examination

#### Examination arrangement: Assignment

Term Status code Evaluation Weighting Examination aids Date Time Examination system
Autumn ORD Assignment 100/100
• * 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.
Examination

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

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