Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Accelerating Two Projection Methods via Perturbations with Application to IntensityModulated Radiation Therapy
 Applied mathematics & optimization 83 (2021), Nr.2, S.881914 ISSN: 00954616 (Print) ISSN: 14320606 (Online) 

 Englisch 
 Zeitschriftenaufsatz 
 Fraunhofer ITWM () 
Abstract
Constrained convex optimization problems arise naturally in many realworld applications. One strategy to solve them in an approximate way is to translate them into a sequence of convex feasibility problems via the recently developed level set scheme and then solve each feasibility problem using projection methods. However, if the problem is illconditioned, projection methods often show zigzagging behavior and therefore converge slowly. To address this issue, we exploit the bounded perturbation resilience of the projection methods and introduce two new perturbations which avoid zigzagging behavior. The first perturbation is in the spirit of kstep methods and uses gradient information from previous iterates. The second uses the approach of surrogate constraint methods combined with relaxed, averaged projections. We apply two different projection methods in the unperturbed version, as well as the two perturbed versions, to linear feasibility problems along with nonlinear optimization problems arising from intensitymodulated radiation therapy (IMRT) treatment planning. We demonstrate that for all the considered problems the perturbations can significantly accelerate the convergence of the projection methods and hence the overall procedure of the level set scheme. For the IMRT optimization problems the perturbed projection methods found an approximate solution up to 4 times faster than the unperturbed methods while at the same time achieving objective function values which were 0.5 to 5.1% lower.