Optimization Algorithms on Matrix Manifolds

This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms.

Optimization algorithms and ODE's in MDO

There is a need for a stronger theoretical understanding of Multidisciplinary Design Optimization (MDO) within the field. Having developed a differential geometry framework in response to this need, we consider how standard optimization algorithms can be modeled using systems of ordinary differential equations (ODEs) while also reviewing optimization algorithms which have been derived from ODE solution methods. We then use some of the framework's tools to show how our resultant systems of ODEs can be analyzed and their behaviour quantitatively evaluated. In doing so, we demonstrate the power and scope of our differential geometry framework, we provide new tools for analyzing MDO systems and their behaviour, and we suggest hitherto neglected optimization methods which may prove particularly useful within the MDO context. Copyright © 2013 by ASME.

Design of triangular lattice photonic crystals using genetic algorithms

Genetic Algorithms (GAs) were used to design triangular lattice photonic crystals with large absolute band-gap. Considering fabricating issues, the algorithms represented the unit cell with large pixels and took the largest absolute band-gap under the fifth band as the objective function. By integrating Fourier transform data storage mechanism, the algorithms ran efficiently and effectively and optimized a triangular lattice photonic crystal with scatters in the shape of 'dielectric-air rod'. It had a large absolute band gap with relative width (ratio of gap width to midgap) 23.8%.

New algorithms of the TSM and TOM methods for calibrating microwave test fixtures

Based on the conventional through-short-match (TSM) method, an improved TSM method has been proposed in this Letter. This method gives an analytical solution and has almost all the advantages of conventional TSM methods. For example, it has no phase uncertainty and no bandwidth limitation. The experimental results show that the accuracy can be significantly improved with this method. The proposed theory can be applied to the through-open-match (TOM) method. (C) 2002 Wiley Periodicals. Inc.

algorithms for computing weak bisimulation equivalence

IEEE Comp Soc, IFIP, Tianjin Normal Univ

The statistic inversion algorithms of water constituents for the Huanghai Sea and the East China Sea

A group of statistical algorithms are proposed for the inversion of the three major components of Case-H waters in the coastal area of the Huanghai Sea and the East China Sea. The algorithms are based on the in situ data collected in the spring of 2003 with strict quality assurance according to NASA ocean bio-optic protocols. These algorithms are the first ones with quantitative confidence that can be applied for the area. The average relative error of the inversed and in situ measured components' concentrations are: Chl-a about 37%, total suspended matter (TSM) about 25%, respectively. This preliminary result is quite satisfactory for Case-H waters, although some aspects in the model need further study. The sensitivity of the input error of 5% to remote sensing reflectance (Rrs) is also analyzed and it shows the algorithms are quite stable. The algorithms show a large difference with Tassan's local SeaWiFS algorithms for different waters, except for the Chl-a algorithm.