# Convex & non-convex constraint sets for full-waveform inversion

 Title Convex & non-convex constraint sets for full-waveform inversion Publication Type SINBAD Presentation Authors Bas Peters, Felix J. Herrmann Publisher SINBAD Year of Publication 2016 Abstract We extend some of our previous work on constrained formulations of full-waveform inversion. Some motivating examples illustrate why solving constrained problems directly is a simpler approach for solving non-linear inverse problems than penalized problem formulations. So far we used constraints which can be represented as convex sets, for which most optimization theory is developed. Some non-convex counterparts of convex sets are introduced and examples show that the algorithms developed for convex sets also work well with non-convex sets. The motivation to also explore non-convex sets, is that they sometimes translate prior geological knowledge into mathematical constraints in a more direct way. All presented material is available as a user-friendly toolbox. The toolbox works with any code which can provide a data-misfit function value and a gradient direction. Keywords Presentation, private, SINBAD, SINBADFALL2016, SLIM URL https://www.slim.eos.ubc.ca/Publications/Private/Conferences/SINBAD/2016/Fall/peters2016SINBADFcnc/peters2016SINBADFcnc.pdf URL1 https://www.slim.eos.ubc.ca/Publications/Private/Conferences/SINBAD/2016... Citation Key peters2016SINBADFcnc