Whether a mathematical model exists or one is inferred from data, it is often of critical interest to determine a set of problem parameters that optimize solution properties. A goal of research in the area of optimization, and a second pillar of the MOCA center, is the design and analysis of algorithms that can find local or global optimizers to problems from models or data.
A complementarity constraint requires that one of a pair of variables should be zero. Optimization problems with complementarity constraints are widespread, arising for example in transportation problems, energy optimization, and sparse optimization.
We investigate the use of nonconvex approaches to rank minimization problems, an alternative to widely-used convex approaches such as nuclear norm minimization.