Institute Matematica Pura e Aplicada IMPA

Rio de Janeiro, Brazil

Institute Matematica Pura e Aplicada IMPA

Rio de Janeiro, Brazil

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Balseiro P.,Institute Matematica Pura e Aplicada IMPA | Marrero J.C.,University of La Laguna | De Diego D.M.,Institute Ciencias Matematicas CSIC UAM UC3M UCM | Padron E.,University of La Laguna
Nonlinearity | Year: 2010

In this paper, we construct Hamilton-Jacobi equations for a large variety of mechanical systems (nonholonomic systems subjected to linear or affine constraints, dissipative systems subjected to external forces, time-dependent mechanical systems etc). We recover all these, in principle, different cases, using a unified framework based on skew-symmetric algebroids with a distinguished 1-cocycle. Several examples illustrate the theory. © 2010 IOP Publishing Ltd&London Mathematical Society.

Bras C.P.,New University of Lisbon | Iusem A.N.,Institute Matematica Pura e Aplicada IMPA | Judice J.J.,Telecommunications Institute of Portugal
Journal of Global Optimization | Year: 2014

We introduce several new results on the Quadratic Eigenvalue Complementarity Problem (QEiCP), focusing on the nonsymmetric case, i.e., without making symmetry assumptions on the matrices defining the problem. First we establish a new sufficient condition for existence of solutions of this problem, which is somewhat more manageable than previously existent ones. This condition works through the introduction of auxiliary variables which leads to the reduction of QEiCP to an Eigenvalue Complementarity Problem in higher dimension. Hence, this reduction suggests a new strategy for solving QEiCP, which is also analyzed in the paper. We also present an upper bound for the number of solutions of QEiCP and exhibit some examples of instances of QEiCP whose solution set has large cardinality, without attaining though the just mentioned upper bound. We also investigate the numerical solution of the QEiCP by exploiting a nonlinear programming and a variational inequality formulations of QEiCP. Some numerical experiments are reported and illustrate the benefits and drawbacks of using these formulations for solving the QEiCP in practice. © 2014 Springer Science+Business Media New York

Iusem A.N.,Institute Matematica Pura e Aplicada IMPA | Martinez-Legaz J.E.,Autonomous University of Barcelona | Todorov M.I.,Universidad de Las Americas Puebla
Journal of Global Optimization | Year: 2013

We introduce and study the family of sets in a finite dimensional Euclidean space which can be written as the Minkowski sum of a compact and convex set and a convex cone (not necessarily closed). We establish several properties of the class of such sets, called Motzkin predecomposable, some of which hold also for the class of Motzkin decomposable sets (i.e., those for which the convex cone in the decomposition is requested to be closed), while others are specific of the new family. © 2013, Springer Science+Business Media New York.

Chen G.-Q.,Fudan University | Chen G.-Q.,University of Oxford | Chen G.-Q.,Northwestern University | Kukreja V.,Northwestern University | And 2 more authors.
Zeitschrift fur Angewandte Mathematik und Physik | Year: 2013

In our previous work, we have established the existence of transonic characteristic discontinuities separating supersonic flows from a static gas in two-dimensional steady compressible Euler flows under a perturbation with small total variation of the incoming supersonic flow over a solid right wedge. It is a free boundary problem in Eulerian coordinates and, across the free boundary (characteristic discontinuity), the Euler equations are of elliptic-hyperbolic composite-mixed type. In this paper, we further prove that such a transonic characteristic discontinuity solution is unique and L 1-stable with respect to the small perturbation of the incoming supersonic flow in Lagrangian coordinates. © 2013 Springer Basel.

Bueno O.,Institute Matematica Pura e Aplicada IMPA | Svaiter B.F.,Institute Matematica Pura e Aplicada IMPA
Mathematical Programming | Year: 2013

Previous examples of non-type (D) maximal monotone operators were restricted to \ell 1, L1, and Banach spaces containing isometric copies of these spaces. This fact led to the conjecture that non-type (D) operators were restricted to this class of Banach spaces. We present a linear non-type (D) operator in c0. © 2013 Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society.

Behling R.,Institute Matematica Pura e Aplicada IMPA | Iusem A.,Institute Matematica Pura e Aplicada IMPA
Mathematical Programming | Year: 2013

We address the problem of solving a continuously differentiable nonlinear system of equations under the condition of calmness. This property, also called upper Lipschitz-continuity in the literature, can be described by a local error bound and is being widely used as a regularity condition in optimization. Indeed, it is known to be significantly weaker than classic regularity assumptions that imply that solutions are isolated. We prove that under this condition, the rank of the Jacobian of the function that defines the system of equations must be locally constant on the solution set. In addition, we prove that locally, the solution set must be a differentiable manifold. Our results are illustrated by examples and discussed in terms of their theoretical relevance and algorithmic implications. © 2011 Springer and Mathematical Optimization Society.

Iusem A.N.,Institute Matematica Pura e Aplicada IMPA
AIP Conference Proceedings | Year: 2010

Consider a real-valued bifunction f which is concave in its first argument and convex in its second one. We study its subdifferential with respect to the second argument, evaluated at pairs of the form (x,x), and the subdifferential of -f with respect to its first argument, evaluated at the same pairs. The resulting operators are not always monotone, and we analyze additional conditions on f which ensure their monotonicity, and furthermore their maximal monotonicity. Our main result is that these operators are maximal monotone when f is continuous and it vanishes whenever both arguments coincide. Our results have consequences in terms of the reformulation of equilibrium problems as variational inequality ones. © 2010 American Institute of Physics.

Cruz L.M.V.,Institute Matematica Pura e Aplicada IMPA | Velho L.,Institute Matematica Pura e Aplicada IMPA
Proceedings - 23rd Conference on Graphics, Patterns and Images Tutorials, SIBGRAPI-T 2010 | Year: 2010

Geometric Modeling is a widely studied area in computer graphics and methods for constructing 3D models with intuitive interfaces are a topic that has been attracting the interest of many researches. In contrast to the complicated interfaces of modeling softwares, created using the WIMP paradigm (Window, Icon, Menu, Pointer), several studies have shown applications with interfaces based on gestures, which are simpler and more natural. In this scenario, the area of Sketch-Based Interfaces and Modeling (SBIM) emerged. Sketch is a very efficient tool to convey the essence of an object with few strokes, because humans have the ability of inferring 3D models from 2D drawings. However, associating a sketch to a 3D model is not a computationally trivial task. In this paper we present a conceptualization of the area, highlighting opportunities, challenges and trends in SBIM. © 2010 IEEE.

Santos A.S.,Federal University of Sergipe | Santos A.S.,Institute Matematica Pura e Aplicada IMPA
Annales Henri Poincare | Year: 2010

It has been showed by Byde (Indiana Univ. Math. J. 52(5):1147-1199, 2003) that it is possible to attach a Delaunay-type end to a compact nondegenerate manifold of positive constant scalar curvature, provided it is locally conformally flat in a neighborhood of the attaching point. The resulting manifold is noncompact with the same constant scalar curvature. The main goal of this paper is to generalize this result. We will construct a one-parameter family of solutions to the positive singular Yamabe problem for any compact non-degenerate manifold with Weyl tensor vanishing to sufficiently high order at the singular point. If the dimension is at most 5, no condition on the Weyl tensor is needed. We will use perturbation techniques and gluing methods. © Birkhäuser / Springer Basel AG 2010.

Ambrozio L.C.,Institute Matematica Pura e Aplicada IMPA
Communications in Mathematical Physics | Year: 2015

In this paper we prove the Penrose inequality for metrics that are small perturbations of the Schwarzschild anti-de Sitter metrics of positive mass. We use the existence of a global foliation by weakly stable constant mean curvature spheres and the monotonicity of the Hawking mass. © 2015, Springer-Verlag Berlin Heidelberg.

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