Evaluating bound-constrained minimization software

Bound-constrained minimization is a subject of active research. To assess the performance of existent solvers, numerical evaluations and comparisons are carried on. Arbitrary decisions that may have a crucial effect on the conclusions of numerical experiments are highlighted in the present work. As a result, a detailed evaluation based on performance profiles is applied to the comparison of bound-constrained minimization solvers. Extensive numerical results are presented and analyzed.

Augmented Lagrangian method with nonmonotone penalty parameters for constrained optimization

At each outer iteration of standard Augmented Lagrangian methods one tries to solve a box-constrained optimization problem with some prescribed tolerance. In the continuous world, using exact arithmetic, this subproblem is always solvable. Therefore, the possibility of finishing the subproblem resolution without satisfying the theoretical stopping conditions is not contemplated in usual convergence theories. However, in practice, one might not be able to solve the subproblem up to the required precision. This may be due to different reasons. One of them is that the presence of an excessively large penalty parameter could impair the performance of the box-constraint optimization solver. In this paper a practical strategy for decreasing the penalty parameter in situations like the one mentioned above is proposed. More generally, the different decisions that may be taken when, in practice, one is not able to solve the Augmented Lagrangian subproblem will be discussed. As a result, an improved Augmented Lagrangian method is presented, which takes into account numerical difficulties in a satisfactory way, preserving suitable convergence theory. Numerical experiments are presented involving all the CUTEr collection test problems.

The boundedness of penalty parameters in an augmented Lagrangian method with constrained subproblems

Augmented Lagrangian methods are effective tools for solving large-scale nonlinear programming problems. At each outer iteration, a minimization subproblem with simple constraints, whose objective function depends on updated Lagrange multipliers and penalty parameters, is approximately solved. When the penalty parameter becomes very large, solving the subproblem becomes difficult; therefore, the effectiveness of this approach is associated with the boundedness of the penalty parameters. In this paper, it is proved that under more natural assumptions than the ones employed until now, penalty parameters are bounded. For proving the new boundedness result, the original algorithm has been slightly modified. Numerical consequences of the modifications are discussed and computational experiments are presented.

Constrained least square pre-distortion scheme for multiuser ultra-wideband

The study proposes a constrained least square (CLS) pre-distortion scheme for multiple-input single-output (MISO) multiple access ultra-wideband (UWB) systems. In such a scheme, a simple objective function is defined, which can be efficiently solved by a gradient-based algorithm. For the performance evaluation, scenarios CM1 and CM3 of the IEEE 802.15.3a channel model are considered. Results show that the CLS algorithm has a fast convergence and a good trade-off between intersymbol interference (ISI) and multiple access interference (MAI) reduction and signal-to-noise ratio (SNR) preservation, performing better than time-reversal (TR) pre-distortion.

Classical magnetoresistance of a ballistic electron gas constrained to non-planar topographies in a lattice of antidots under tilted magnetic field

The classical magnetoresistance of a two-dimensional electron gas constrained to non-planar topographies, in antidot lattices, and under the influence of tilted magnetic field in arbitrary direction is numerically studied. (C) 2012 Elsevier B.V. All rights reserved.

GREEN MACHINING ORIENTED TO DIMINISH DENSITY GRADIENT FOR MINIMIZATION OF DISTORTION IN ADVANCED CERAMICS

After sintering advanced ceramics, there are invariably distortions, caused in large part by the heterogeneous distribution of density gradients along the compacted piece. To correct distortions, machining is generally used to manufacture pieces within dimensional and geometric tolerances. Hence, narrow material removal limit conditions are applied, which minimize the generation of damage. Another alternative is machining the compacted piece before sintering, called the green ceramic stage, which allows machining without damage to mechanical strength. Since the greatest concentration of density gradients is located in the outer-most layers of the compacted piece, this study investigated the removal of different allowance values by means of green machining. The output variables are distortion after sintering, tool wear, cutting force, and the surface roughness of the green ceramics and the sintered ones. The following results have been noted: less distortion is verified in the sintered piece after 1mm allowance removal; and the higher the tool wear the worse the surface roughness of both green and sintered pieces.