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 - 3

Total - Available soon

Teaching language



Linear Optimization and Calculus.


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

Available soon

Evaluation method

The evaluation will be done through  two presential exams (one in the middle of the semester and the  other one at the end) and several homework assignments (approximately 6), each one including  a theoretical  and a practical part.

Each exam represents 30 percent of the final grade, and the average of the homework assigments represents the remaining 40 percent.

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.


Programs where the course is taught: