09h00 - 10h00
Random Projections in Mathematical Programming: Survey and New Directions
Random projections are random matrices that decrease the dimensionality of a finite set of vectors while guaranteeing approximate congruence of the high and low dimensional point sets. Their application to Mathematical Programming yields projected formulations with fewer constraints or variables (or, occasionally, both), which can be solved faster than their full-dimensional counterparts, and provide: reasonable bounds on the optimal value, and approximately feasible solutions. I am going to provide a summary of the work done so far in LP, SDP, QP, then discuss current work.