Complementarity is ubiquitous in the natural and social sciences. It is a fundamental principle underlying equilibrium. In a primal-dual description of a system it means that either the pri- mal or the corresponding dual component of the solution vector must vanish. There are many pro- blems that can be naturally modeled as complemen- tarity problems (CPs). Applications of complemen- tarity problems are prevalent, especially in econo- mics and engineering. (More...)

The max-cut algorithm of Goemans and Williamson is 15 years old in 2009, and its impact in the area of semidefinite programming has been remarkable. In this talk, I will survey some of the main modelling and algorithmic developments since 1994 in the application of semidefinite programming to discrete optimization problems. I will also highlight promising directions for research in this area.

We introduce a discrete-time fractional calculus of variations. First and second order necessary optimality conditions are established. Exam- ples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. They show that the solutions of the fractional problems coincide with the solutions of the corresponding non fractional variational problems when the order of the discrete derivatives is an integer value.

This talk is about constrained impulsive control problems in which we propose a new mathematical concept of control required for impulsive context. These controls that we consider may arise in engineering, in particular, in problems of space navigation. Necessary conditions of extremum in the form of the Pontryagin’s Maximum Principle are studied.

The Q-index (or spectral radius) of a simple graph is the largest eigenvalue of its signless Laplacian matrix. There are many results in the literature where, for some fixed class of graphs, all graphs whose index is maximal are identified. For connected graphs of fixed order and size this pro- blem is not yet completely resolved (in contrast to the more general class when connectivity is not re- quired). It is only known (for a long time) that the graphs with maximal Q-index in the former class (and the latter one) are the nested split graphs. Focusing our attention on eigenvector techniques we got some new (lower and upper) bounds on the Q-index of nested split graphs.

A análise de documentos estruturados, como é o caso dos documentos anotados em XML, é fundamental para a sua compreensão que é requerida em todas as tarefas de manutenção e reutilização. A manutenção é exigida no dia-a-dia para corrigir defeitos, precaver problemas e adicionar funcionalidades. A reutilização mostra-se relevante para economia de custos e rentabilização.(...)

Recently I had a short scientific visit to the acoustics research institute in Vienna. My objective was to communicate with mathematicians who work closely with sound engineers in order to pick up some statements of interesting mathematical problems. During this talk I intend to share the results of this experience.

We focus on the minimal time control problem for single-input control-affine systems dx/dt = X(x) + u1Y1(x) pertece R^n, where the scalar control u1 fulfills the constraint ju1(:)j^t=1. We recall the concept of conjugate time for the bang-bang case in these systems and propose an asymptotic approach, based on a penalized procedure, which allows the application of the well-known results (theoretical and practical) on the conjugate times for the smooth case into the bang-bang case.