Non Linear Optimization


The goals are:

1- To distinguish the problems by degree of difficulty.

2 - To know optimality conditions and methods for local optima.

3- To understand how the methods "work" for problems with and without constraints, and to be able to compare their merits and weaknesses and convergence rate.

4- To understand the application of some methods for special problems like least squares.

5- To be have an overview of global optimization methods.

General characterization





Responsible teacher

Paula Alexandra da Costa Amaral


Weekly - 4

Total - 60

Teaching language



Calculus, Taylor Formula, partial derivatives.


Bertsekas, Dimitri P. (1995) -  “Nonlinear Programming”,Athena Scientific;


Nash, Stephen G.; Sofer, Ariela, (1996) – “Linear and Nonlinear Programming”, McGraw-Hill;


Nocedal, Jorge; Wright, Stephen J., (1999) – “Numerical Optimization”, Springer-Verlag.

Teaching method

 Theoretical practical classes.

Evaluation method

There is no frequency classification. Continuous assessment is carried out by the delivery of two individual practical assignments whose grade is worth 40% ad a written test whose grade is worth 60% for the final score. The minimum grade for the written test is 7 points. At the time of resit, the student can perform or improve the assessment corresponding to the written test, keeping the grades of the work or not. Also on the resit, if you take the average with the works, it is necessary to have at least 7 values in the written exam. In the special season, the written evaluation is worth 100% of the final grade.

Subject matter

1- Introduction

  • Formulation of problems
  • graphical resolution of simple problems
  • Rates of convergence

2 Unconstrained Problems

  • Necessary and sufficient optimality conditions
  • Newton method and gradient descent .
  • Line search methods.Armijo and Wolfe conditions
  • Trust region methods.
  • Quasi-Newton methods.The BFGS formula.


3 Constrained optimisation

  • Necessary and sufficient optimality conditions
  • Active set method
  • Lagrangean Dual
  • KKT conditions

4 Quadratic Programming.

5 Penalities, Barrier and augmented Lagrangian methods.

 6 Least Squares Problems

7  Brief introduction to global optimization.