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Seminários do IMPA

Otimização

Título |
Linear Complementarity Problems: Applications, Formulations and Algorithms |

Expositor |
Joaquim Júdice
Universidade de Coimbra |

Data |
Quarta-feira, 7 de junho de 2017, 15:30 |

Local |
Sala 345 |

Resumo |

The Linear Complementarity Problem (LCP) consists of finding two nonnegative vectors

satisfying linear constraints and complementarity conditions between pairs of components of

the same order. The LCP has found many applications in several areas of science, engineering,

finance and economics. In this talk the LCP and some important extensions of this problem are

first introduced together with some of their most relevant properties and applications.

A number of formulations of optimization problems are shown to be formulated as an LCP or

one of its extensions. These include Linear and Quadratic Programming, Affine Variational

Inequalities, Bilevel Programming, Bilinear Programming, 0-1 Integer Programming, Fixed-

Charge Problems, Absolute Value Programming, Copositive Programming, Fractional Quadratic

Programming, Linear and Total Least-Squares Problems, Eigenvalue Complementarity Problems,

Matrix Condition Number Estimation, Clique and Independent Numbers of a Graph and

Mathematical Programming with Cardinality Constraints. The most relevant algorithms for

solving LCP and its extensions are briefly reviewed. The benefits and drawbacks of solving these

optimization problems by using complementarity algorithms applied to their formulations are

discussed.