CORE Seminar: Peter Bür­gisser

The analy­sis of the sta­bil­ity and effi­ciency of algo­rithms for con­vex opti­miza­tion nat­u­rally leads to the study of con­di­tion num­bers. The Grass­mann con­di­tion, which is a geo­met­ric ver­sion of Renegar’s con­di­tion, is espe­cially suited for a prob­a­bilis­tic analy­sis. Such analy­sis can be per­formed by rely­ing on tech­niques from spher­i­cal con­vex geom­e­try and dif­fer­en­tial geom­e­try. Along this way, we obtain an aver­age analy­sis of the Grass­mann con­di­tion num­ber that holds for any reg­u­lar con­vex cone. A closer look prompts the inves­ti­ga­tion of the spher­i­cal coun­ter­parts of intrin­sic vol­umes — a notion thor­oughly stud­ied for euclid­ean spaces, but much less so for spheres, so that many fas­ci­nat­ing ques­tions remain.

Joint work with Den­nis Amelunxen.