Multiobjective Optimisation Program PhD

Multiobjective Optimization




Prof. Matteo Rocca.


Office hours: by appointment.




In this course we understand the solution of a decision problem as to choose “good” or “best” among a set of “alternatives” in risk free context, where we assume the existence of certain criteria, according to which the quality of the alternatives is measured. After introducing the concept of binary relation, the course will  focus on complete orders (i.e. preference relations) and then on partial orders which will motivate the study of multiobjective optimization.


Course Description


Convex sets, hyperplanes, separation theorems, convex functions, properties of convex functions. Binary relations, orders, complete orders and preference relations, choice rules. Utility functions and preference relations: Debreu’s representation Theorem. Scalar optimization, convex optimization. Partial orders and multiobjective optimization: partial orders and cones, efficient, weakly efficient and proper solutions. Linear scalarization, Pareto reducibility, optimality conditions for multiobjective optimization problems. Convex multiobjective optimization problems.



There are only three grades for this course: failure; pass; pass with distinction.

Evaluation rules will be communicated during the course.



Reading materials


  • Course readings.
    • Mas Colell, Whinston, Green, Microeconomic Theory, Oxford University Press, 1995, Chapters 1,2, 3; Mathematical Appendix;
    • Boyd, Vandenberghe, Convex Optimization, Cambridge University Press, 2009, Chapters 1,2,3,4;
    • Yu, Multiple Criteria Decision Making, Plenum Press, 1985, Chapters 1,2,3.
    • Lowe, Thisse, Ward, Wendell, On efficient solutions to multiple objective mathematical programs, Management Sci., 30 (1984), 1346–1349.
    • Further readings will be communicated during the course.
  • Background readings. Students should be familiar with the topics of the following readings before attending the course.
    • Simon, Blume, Mathematics for Economists, Norton and Company, 1994;
    • Hoy, Livernois, McKenna, Rees, Stengos, Mathematics for Economics, 2nd Edition, The MIT Press.
    • Mas Colell, Whinston ,Green, Microeconomic Theory, Oxford University Press, 1995, Mathematical Appendix.


The reading materials can be found in the university library (, or in the internet.



All meetings will take place in the Seminar Room, Department of Economics, Via Monte Generoso 71, first floor.



Class #1: January 15, 2016, 10.30-13.30

Class #2: January 21, 2016, 14.30-17.30

Class #3: January 29, 2016, 10.30-13.30

Class #4: February 2, 2016, 14.30-17.30

Class #5: February 16, 2016, 10.30-13.30