Francisco A. M. Gomes

Nonlinear programming algorithms using trust regions and augmented Lagrangians with nonmonotone penalty parameters

The strategy for obtaining global convergence is based on the trust region approach. The merit function is a type of augmented Lagrangian. A new updating scheme is introduced for the penalty parameter, by means of which monotone increase is not necessary.Global convergence results are proved and numerical experiments are presented.

Dynamic Control of Infeasibility in Equality Constrained Optimization

This paper describes a new algorithm for solving nonlinear programming problems with equality constraints. The method introduces the idea of using trust cylinders to keep the infeasibility under control. Each time the trust cylinder is violated, a restoration step is called and the infeasibility level is reduced. The radius of the trust cylinder has a nonincreasing update scheme, so eventually a feasible (and optimal) point is obtained. Global and local convergence of the algorithm are analyzed, as well as its numerical performance. The results suggest that the algorithm is promising.

An SLP algorithm and its application to topology optimization

We introduce a globally convergent sequential linear programming method for nonlinear programming. The algorithm is applied to the solution of classic topology optimization problems, as well as to the design of compliantmechanisms. The numerical results suggest that the new algorithm is faster than the globally convergent version of the method of moving asymptotes, a popular method for mechanical engineering applications proposed by Svanberg.

Solution of a truss topology bilevel programming problem by means of an inexact restoration method

We formulate a truss topology optimization problem as a bilevel programming problem and solve it by means of a line search type inexact restoration algorithm. We discuss details of the implementation and show results of numerical experiments.

ProFIS: A New Paradigm for Higher Education in Brazil

Public universities represent nowadays a relatively small part of the Brazilian higher education system, both in terms of number of institutions and in terms of enrolment. Approximately 3/4 of all undergraduate students in Brazil attend private institutions. Public institutions are, on average, much more selective than those in the private system. This profile has two basic causes: the higher prestige of public universities and the fact that they do not charge any tuition fees. However, many of the students who are accepted at public universities come from wealthy families, and relatively fewer are from poor families or from minority groups, such as afro-descendents. The higher selectivity has a clear effect of inhibiting them from applying to a public Higher Education Institution (HEI), as we will see in the case of the University of Campinas (Unicamp), one of the most selective universities in Brazil.

Preconditioning by projectors in the solution of contact problems : a parallel implementation

A non-overlapping domain decomposition algorithm of the Neumann–Neumann type for solving contact problems of elasticity is presented. Using the duality theory of convex programming, the discretized problem turns into a quadratic one with equality and bound constraints. The dual problem is modified by orthogonal projectors to the natural coarse space. The resulting problem is solved by an augmented Lagrangian algorithm. The projectors ensure an optimal convergence rate for the solution of the auxiliary linear problems by the preconditioned conjugate gradient method. Relevant aspects on the numerical linear algebra of these problems are presented, together with an efficient parallel implementation of the method.

Parallel implementations of Broyden's method

Broydens method is one of the most effective algorithms for solving nonlinear systems of equations. When the number of equations and unknowns is very large, memoryless implementations of this method are frequently used. We analyze one of this implementations (Gomes-Ruggiero, Martínez and Moretti, SIAM J. Sci. Stat. Comput. 1991, to appear) and we show that calculations may be organized in such a way that parallelism can be exploited.ZusammenfassungDas Verfahren von Broyden liefert einen der effizientesten Algorithmen zur Lösung nichtlinearer Gleichungssysteme. Bei sehr vielen Gleichungen und Unbekannten werden häufig Implementierungen ohne Zwischenspeicherung verwendet (Gomes-Ruggiero, Martinez und Moretti, SIAM J. SCISC 91, erscheint in Kürze). Wir zeigen, daß die Rechnungen so organisiert werden können, daß man ihren Parallelismus ausnützen kann.