Constrained dogleg methods for nonlinear systems with simple bounds

We focus on the numerical solution of medium scale bound-constrained systems of nonlinear equations. In this context, we consider an affine-scaling trust region approach that allows a great flexibility in choosing the scaling matrix used to handle the bounds. The method is based on a dogleg procedure tailored for constrained problems and so, it is named Constrained Dogleg method. It generates only strictly feasible iterates. Global and locally fast convergence is ensured under standard assumptions. The method has been implemented in the Matlab solver CoDoSol that supports several diagonal scalings in both spherical and elliptical trust region frameworks. We give a brief account of CoDoSol and report on the computational experience performed on a number of representative test problem

PROFIT: a new alternative for emission-line PROfile FITting

I briefly describe a simple routine for emission-line profiles fitting by Gaussian curves or Gauss-Hermite series. The PROFIT (line-PROfile FITting) routine represent a new alternative for use in fits data cubes, as those from Integral Field Spectroscopy or Fabry-Perot Interferometry, and may be useful to better study the emission-line flux distributions and gas kinematics in distinct astrophysical objects, such as the central regions of galaxies and star forming regions. The PROFIT routine is written in IDL language and is available at http://www.ufsm.br/rogemar/software.html. The PROFIT routine was used to fit the [Fe II]1.257um emission-line profiles for about 1800 spectra of the inner 350 pc of the Seyfert galaxy Mrk1066 obtained with Gemini NIFS and shows that the line profiles are better reproduced by Gauss-Hermite series than by the commonly used Gaussian curves. The two-dimensional map of the h_3 Gauss-Hermite moment shows its highest absolute values in regions close to the edge of the radio structure. These high values may be originated in an biconical outflowing gas associated with the radio jet - previously observed in the optical [O III] emission. The analysis of this kinematic component indicates that the radio jet leaves the center of the galaxy with the north-west side slightly oriented towards us and the south-east side away from us, being partially hidden by the disc of the galaxy.Comment: Accepted for publication Astrophysics & Space Science - 7 pges; 4 Fig

Multiagent cooperation for solving global optimization problems: an extendible framework with example cooperation strategies

This paper proposes the use of multiagent cooperation for solving global optimization problems through the introduction of a new multiagent environment, MANGO. The strength of the environment lays in itsflexible structure based on communicating software agents that attempt to solve a problem cooperatively. This structure allows the execution of a wide range of global optimization algorithms described as a set of interacting operations. At one extreme, MANGO welcomes an individual non-cooperating agent, which is basically the traditional way of solving a global optimization problem. At the other extreme, autonomous agents existing in the environment cooperate as they see fit during run time. We explain the development and communication tools provided in the environment as well as examples of agent realizations and cooperation scenarios. We also show how the multiagent structure is more effective than having a single nonlinear optimization algorithm with randomly selected initial points

Algorithms for bound constrained quadratic programming problems. Numer. Math. 55 (1989), no. 4, 377--400

We present an algorithm which combines standard active set strategies with the gradient projection method for the solution of quadratic programming problems subject to bounds. We show, in particular, that if the quadratic is bounded below on the feasible set then termination occurs at a stationary point in a finite number of iterations. Moreover, if all stationary points are nondegenerate, termination occurs at a local minimizer. A numerical comparison of the algorithm based on the gradient projection algorithm with a standard active set strategy shows that on mildly degenerate problems the gradient projection algorithm requires considerable less iterations and time than the active set strategy. On nondegenerate problems the number of iterations typically decreases by at least a factor of 10. For strongly degenerate problems, the performance of the gradient projection algorithm deteriorates, but it still performs better than the active set method