A modified standard embedding with jumps in nonlinear optimization

The paper deals with a combination of pathfollowing methods (embedding approach) and feasible descent direction methods (so-called jumps) for solving a non-linear optimization problem with equality and inequality constraints. Since the method that we propose here uses jumps from one connected component to another one, more than one connected component of the solution set of the corresponding one-parametric problem can be followed numerically. It is assumed that the problem under consideration belongs to a generic subset which was introduced by Jongen, Jonker and Twilt. There already exist methods of this type for which each starting point of a jump has to be an endpoint of a branch of local minimizers. In this paper the authors propose a new method by allowing a larger set of starting points for the jumps which can be constructed at bifurcation and turning points of the solution set. The topological properties of those cases where the method is not successful are analyzed and the role of constraint qualifications in this context is discussed. Furthermore,this new method is applied to a so-called modified standard embedding which is a particular construction without equality constraints. Finally, an algorithmic version of this new method as well as computational results are presented

A NOTE ON LOGARITHMIC SMOOTHING IN SEMI-INFINITE OPTIMIZATION UNDER REDUCTION APPROACH*

This note deals with a semi-infinite optimization problem which is defined by infinitely many inequality constraints. By applying a logarithmic barrier function, a family of interior point approximations of the feasible set is obtained where locally the original feasible set and its approximations are homeomorphic. Under generic assumptions on the structure of the original feasible set, strongly stable stationary points of the original problem are considered and it is shown that there is a one-to-one correspondence between the stationary points (and their stationary indices) of the original problem and those of its approximations. Corresponding convergence results, global aspects and a relationship to a standard interior-point approach are discussed

Automated analysis of digital fundus autofluorescence images of geographic atrophy in advanced age-related macular degeneration using confocal scanning laser ophthalmoscopy (cSLO)

BACKGROUND: Fundus autofluorescence (AF) imaging using confocal scanning laser ophthalmoscopy (cSLO) provides an accurate delineation of areas of geographic atrophy (GA). Automated computer-assisted methods for detecting and removing interfering vessels are needed to support the GA quantification process in longitudinal studies and in reading centres. METHODS: A test tool was implemented that uses region-growing techniques to segment GA areas. An algorithm for illuminating shadows can be used to process low-quality images. Agreement between observers and between three different methods was evaluated by two independent readers in a pilot study. Agreement and objectivity were assessed using the Bland-Altman approach. RESULTS: The new method (C) identifies vascular structures that interfere with the delineation of GA. Results are comparable to those of two commonly used procedures (A, B), with a mean difference between C and A of -0.67 mm(2 )(95% CI [-0.99, -0.36]), between B and A of -0.81 mm(2), (95% CI [-1.08, -0.53]), and between C and B of 0.15 mm(2 )(95% CI [-0.12, 0.41]). Objectivity of a method is quantified by the mean difference between observers: A 0.30 mm(2 )(95% CI [0.02, 0.57]), B -0.11 mm(2 )(95% CI [-0.28, 0.10]), and C 0.12 mm(2 )(95% CI [0.02, 0.22]). CONCLUSION: The novel procedure is comparable with regard to objectivity and inter-reader agreement to established methods of quantifying GA. It considerably speeds up the lengthy measurement process in AF with well defined GA zones

Coherent Propagation of Polaritons in Semiconductor Heterostructures: Nonlinear Pulse Transmission in Theory and Experiment

The influence of coherent optical nonlinearities on polariton propagation effects is studied within a theory-experiment comparison. A novel approach that combines a microscopic treatment of the boundary problem in a sample of finite thickness with excitonic and biexcitonic nonlinearities is introduced. Light-polarization dependent spectral changes are analyzed for single-pulse transmission and pump-probe excitation

Scanning Laser Ophthalmoscopy (SLO)

Since the first scanning laser ophthalmoscope (SLO) was introduced in the early 1980s, this imaging technique has been adapted and optimized for various clinical applications based on different contrast mechanism. Reflectance imaging, where the back scattered light is detected, is widely used for eye tracking and as reference image for OCT applications. But also the reflectance modality itself has several important diagnostic applications: laser scanning tomography (SLT), imaging with different laser wavelengths (Multicolor contrast) and others. Fluorescence imaging channels with different excitation wavelengths were introduced to SLOs for angiography, i.e. for the visualization of the vascular system after intravenously injecting an appropriate dye, as well as for autofluorescence imaging of endogenous fluorophores within the retina