An algorithme for quadratic optimization with one quadratic constraint and bounds on the variables

This paper presents an efficient algorithm to solve a constrained optimisation problem with a quadratic object function, one quadratic constraint and (positivity) bounds on the variables. Against little computational cost, the algorithm allows for the inclusion of positivity of the solution as prior knowledge. This is very useful for the solution of those (linear) inverse problems where negative solutions are unphysical. The algorithm rewrites the solution as a function of the Lagrange multipliers, which is achieved with the help of the generalised eigenvectors, or equivalently, the generalised singular value decomposition. The next step is to find the Lagrange multipliers. The multiplier corresponding to the quadratic constraint, which is known to be active, is easy to find. The Lagrange multipliers corresponding to the positivity constraints are found with an iterative method that can be likened to the activeset methods from quadratic programming

An algorithme for quadratic optimization with one quadratic constraint and bounds on the variables

This paper presents an efficient algorithm to solve a constrained optimisation problem with a quadratic object function, one quadratic constraint and (positivity) bounds on the variables. Against little computational cost, the algorithm allows for the inclusion of positivity of the solution as prior knowledge. This is very useful for the solution of those (linear) inverse problems where negative solutions are unphysical. The algorithm rewrites the solution as a function of the Lagrange multipliers, which is achieved with the help of the generalised eigenvectors, or equivalently, the generalised singular value decomposition. The next step is to find the Lagrange multipliers. The multiplier corresponding to the quadratic constraint, which is known to be active, is easy to find. The Lagrange multipliers corresponding to the positivity constraints are found with an iterative method that can be likened to the activeset methods from quadratic programming

A model-independent algorithm for ionospheric tomography 1 : theory and tests

This paper presents a model-independent algorithm for tomography of the ionosphere. The prior knowledge consists of the following pieces of information: electron density cannot be negative, the ionosphere is basically smooth and stratified and electron density is low at high (more than aproximately 700 km) and low (less than approximately 100 km) altitude.Tests based on simulated measurements show that the method recovers the latitudinal structure well, whereas the vertical structure is recovered with moderate success: the estimated height of the layer of maximum electron density may be as much as 90 km in error. Because of the imposed smoothness, the method tends to underestimate the peak in electron density, by as much as one third in unfavorable cases

A model-independent algorithm for ionospheric tomography 2 : experimental results

This paper presents the results of an ionospheric tomography experiment over mid-latitude Europe. The campaign has yielded 539 reconstructions over a 45 day period in spring 1995. Special attention is paid to the performance of the reconstruction algorithm, specifically by comparison with ionosonde data. Tomography and soundings tend to agree on electron density, but they do not agree on the height of maximum electron density: tomography seems to overestimate Hmax. Whereas tomography finds a daily oscillation in Hmax between 250 km (daytime) and 450 km (nighttime), the soundings indicate an oscillation between 200 and 250 km.

Warm IRAS sources from the point source catalog. IV. Extended optical line emission

Wetensch. publicatieFaculteit der Wiskunde en Natuurwetenschappe