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Code: | PDEEC0005 | Acronym: | VSM |

Keywords | |
---|---|

Classification | Keyword |

OFICIAL | Electrical and Computer Engineering |

Active? | Yes |

Responsible unit: | Department of Electrical and Computer Engineering |

Course/CS Responsible: | Doctoral Program in Electrical and Computer Engineering |

Acronym | No. of Students | Study Plan | Curricular Years | Credits UCN | Credits ECTS | Contact hours | Total Time |
---|---|---|---|---|---|---|---|

PDEEC | 3 | Syllabus since 2015/16 | 1 | - | 7,5 | 70 | 202,5 |

Teacher | Responsibility |
---|---|

Maria do Rosário Marques Fernandes Teixeira de Pinho |

Recitations: | 3,00 |

Type | Teacher | Classes | Hour |
---|---|---|---|

Recitations | Totals | 1 | 3,00 |

Maria do Rosário Marques Fernandes Teixeira de Pinho | 3,00 |

spaces .

2- Normed linear spaces, open and closed sets; convergence; continuity; Banach

spaces, Complete subsets, Quotient spaces, Denseness and Separability

3- Fixed points of transformations on Banach Spaces -- Applications to solutions of

ordinary differential and integral equations

4- Hilbert Spaces -- The Projection Theorem; Orthogonal Complements; Gram-Schmidt

Procedure; Minimum distance to a convex set

5- Hilbert Spaces of random variables and stochastic processes; Least-squares

estimation

6- Dual Spaces. The Hahn-Banach Theorem, with applications to minimum norm

problems

7- Linear operators and adjoints

8- Optimization of functionals -- General results on existence and uniqueness of an optimum

9- Optimization of functionals. Gateaux and Frechet derivatives. Extrema; Euler-

Lagrange equations; Min-Max Theorem in Game Theory.

10- Constrained optimization of functionals: Global theory; Convex-concave functionals,

conjugate functionals, dual optimization problems, Lagrange multipliers, sufficiency;

sensitivity, duality; applications .

11- Constrained Optimization; Equality and Inequality Constraints; Kuhn-Tucker´Theorem in infinite dimensions

12- Other related topics (as time permits)

Polak, E; Optimization: Algorithms and Consistent Approximations, Springer, New York, 1997. ISBN: 0-387-94971-2

Boyd, S. and Vandenberghe, L; Convex Optimization, Cambridge University Press, 2005. ISBN: 0 521 83378 7

Varaiya, Pravin; Lecture notes on optimization, e-book, http://paleale.eecs.berkeley.edu/~varaiya/papers_ps.dir/NOO.pdf

Designation | Weight (%) |
---|---|

Participação presencial | 20,00 |

Trabalho escrito | 80,00 |

Total: |
100,00 |

Designation | Time (hours) |
---|---|

Estudo autónomo | 100,00 |

Trabalho escrito | 50,00 |

Total: |
150,00 |

week after being assigned.

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Page generated on: 2020-03-29 at 17:19:37

Page generated on: 2020-03-29 at 17:19:37