Inexact Newton Dogleg Methods

The dogleg method is a classical trust-region technique for globalizing Newton\u27s method. While it is widely used in optimization, including large-scale optimization via truncated-Newton approaches, its implementation in general inexact Newton methods for systems of nonlinear equations can be problematic. In this paper, we first outline a very general dogleg method suitable for the general inexact Newton context and provide a global convergence analysis for it. We then discuss certain issues that may arise with the standard dogleg implementational strategy and propose modified strategies that address them. Newton-Krylov methods have provided important motivation for this work, and we conclude with a report on numerical experiments involving a Newton-GMRES dogleg method applied to benchmark CFD problems

Coupling problem in thermal systems simulations

Building energy simulation is playing a key role in building design in order to reduce the energy consumption and, consequently, the CO2 emissions. An object-oriented tool called NEST is used to simulate all the phenomena that appear in a building. In the case of energy and momentum conservation and species transport, the current solver behaves well, but in the case of mass conservation it takes a lot of time to reach a solution. For this reason, in this work, instead of solving the continuity equations explicitly, an implicit method based on the Trust Region algorithm is proposed. Previously, a study of the properties of the model used by NEST-Building software has been done in order to simplify the requirements of the solver. For a building with only 9 rooms the new solver is a thousand times faster than the current method

MIMO CDMA-based Optical SATCOMs: A New Solution

A new scheme for MIMO CDMA-based optical satellite communications (OSATCOMs) is presented. Three independent problems are described for up-link and down- link in terms of two distinguished optimization problems. At first, in up-link, Pulse-width optimization is proposed to reduce dispersions over fibers as the terrestrial part. This is performed for return-to-zero (RZ) modulation that is supposed to be used as an example in here. This is carried out by solving the first optimization problem, while minimizing the probability of overlapping for the Gaussian pulses that are used to produce RZ. Some constraints are assumed such as a threshold for the peak-to-average power ratio (PAPR). In down-link, the second and the third problems are discussed as follows, jointly as a closed-form solution. Solving the second optimization problem, an objective function is obtained, namely the MIMO CDMA-based satellite weight-matrix as a conventional adaptive beam-former. The Satellite link is stablished over flat un-correlated Nakagami-m/Suzuki fading channels as the second problem. On the other hand, the mentioned optimization problem is robustly solved as the third important problem, while considering inter-cell interferences in the multi-cell scenario. Robust solution is performed due to the partial knowledge of each cell from the others in which the link capacity is maximized. Analytical results are conducted to investigate the merit of system.Comment: IEEE PCITC 2015 (15-17 Oct, India

On affine scaling inexact dogleg methods for bound-constrained nonlinear systems

Within the framework of affine scaling trust-region methods for bound constrained problems, we discuss the use of a inexact dogleg method as a tool for simultaneously handling the trust-region and the bound constraints while seeking for an approximate minimizer of the model. Focusing on bound-constrained systems of nonlinear equations, an inexact affine scaling method for large scale problems, employing the inexact dogleg procedure, is described. Global convergence results are established without any Lipschitz assumption on the Jacobian matrix, and locally fast convergence is shown under standard assumptions. Convergence analysis is performed without specifying the scaling matrix used to handle the bounds, and a rather general class of scaling matrices is allowed in actual algorithms. Numerical results showing the performance of the method are also given