# Linear Optimization

## Objectives

(i) Improving modeling skills.

(ii) Comprehension of the main concepts and techniques from LP and IP.

(iii) Improving mathematical maturity.

## General characterization

10983

6.0

##### Responsible teacher

Jorge Orestes Lasbarrères Cerdeira

Weekly - 5

Total - 70

Português

### Prerequisites

Students should have knowledge in Linear Algebra, Calculus, and have some skills on algorithms.

### Bibliography

Operations Research: Applications and Algorithms, Wayne L. Winston, Brooks/Cole; 4th edition edition, 2004.

Introduction to Mathematical Optimization, Matteo Fischetti, Kindle Direct Publishing, 2019.

A First Course in Linear Optimization, Jon Lee, Reex Press, 4th edition, 2013-2021 https://github.com/jon77lee/JLee_LinearOptimizationBook/blob/master/JLee.4.01.pdf

### Teaching method

Classes are theoretical/practical with oral presentation of concepts, methodologies, and examples, complemented with problem solving. Specific student difficulties will be addressed during classes or in individual sessions scheduled with the teacher.

Continuous evaluation is based on two tests. If a student does not obtain approval through continuous evaluation he can try it in an additional examination.

### Evaluation method

Rules of evaluation

The student may be evaluated by two tests, each scored 10, and will be approved if  the two tests sum up (rounded) at least 10. The grade will be the rounded sum of the tests.

The student may also be approved by a final exam if the exam''''''''s grade is at least 10. The grade will be the one attained in the exam (rounded) and any grade in any test will be discarded.

## Subject matter

Linear programming (LP): problem formulation, LP geometry, the simplex algorithm, duality, sensitivity analysis.

Integer linear programming (IP): problem formulation, LP vs IP, relaxations, the branch and bound method, heuristics, computational complexity.

## Programs

Programs where the course is taught: