High-Dimensional Data Analysis with Low-Dimensional Models Principles, Computation, and Applications

In Chapter 8, we introduced optimization techniques that efficiently solve many convex optimization problems that arise in recovering structured signals from incomplete or corrupted measurements, using known low-dimensional models. In contrast, as we saw in Chapter 7, problems associated with learning low-dimensional models from sample data are often nonconvex: either they do not have tractable convex relaxations or the nonconvex formulation is preferred due to physical or computational constraints (such as limited memory). In this chapter, we introduce optimization algorithms for nonconvex programs.