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Linear Complementarity Problems: Applications, Formulations and Algorithms
Joaquim Júdice

Universidade de Coimbra
Quarta-feira, 7 de junho de 2017, 15:30
Sala 345

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