Pacific Institute for the Mathematical Sciences - PIMS

Con­di­tion of Con­vex Opti­miza­tion and Spher­i­cal Intrin­sic Vol­umes

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.

Location: EEB 125

The CORE Sem­i­nar is an inter­de­part­men­tal talks series focused on opti­miza­tion, machine learn­ing, big data, sta­tis­tics and numer­ics. This new cross cam­pus activ­ity aims to lever­age the newly estab­lished crit­i­cal mass of fac­ulty and stu­dents in these areas at UW. CORE sem­i­nar is funded in 2014–2015 by Pacific Insti­tute of Math­e­mat­i­cal Sci­ences (PIMS) and the UW Deans of Engi­neer­ing and Arts and Sci­ences. In 2013–14, it was funded by the depart­ments of Math­e­mat­ics, Sta­tis­tics, Elec­tri­cal Engi­neer­ing, and Com­puter Sci­ence Engi­neer­ing, and the deans of Engi­neer­ing and Arts and Sciences.