Linear Optimization


(i) Improving modeling skills.

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

(iii) Improving mathematical maturity.


General characterization





Responsible teacher

Isabel Cristina Silva Correia


Weekly - 4

Total - 56

Teaching language



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


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

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

Only students with frequency will receive a final grade in this course unit.



Frequency is granted to any student who attends at least 2/3 of the classes taught 

Rules of evaluation:

1) There will be two evaluation tests during the semester. Let CT1 and CT2 be the scores in the first and second test respectively, in the scale 0-10. The student will pass the course if CT1+CT2 >= 9.5.

2) Students who have failed in the continuous evaluation may take the final exam covering all the topics taught. Let CE be the score in the exam, in the scale 0-20. The student will pass the course if CE >=  9.5.

3) Students who have already passed the course are eligible for course grade improvement via the final exam. In this case students must sign up beforehand in the "Divisão Académica".

4)  Students with a grade greater than 17 can choose between getting a final grade of 17 or taking a complementary examination to defend the grade.

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.