Abstract / truncated to 115 words (read the full abstract)

This dissertation is concerned with the design and analysis of approximation-based methods for nonconvex nonsmooth optimization problems. The main idea behind those methods is to solve a difficult optimization problem by converting it into a sequence of simpler surrogate/approximate problems. In the two widely-used optimization frameworks, namely, the majorization-minimization (MM) framework and the successive convex approximation (SCA) framework, the approximate function is designed to be a global upper bound, called majorizer, of the original objective function and convex, respectively. Generally speaking, there are two desiderata of the approximate function, i.e., the tightness to the original objective function and the low computational complexity of minimizing the approximate function. In particular, we focus on techniques that can ... toggle 8 keywords

successive convex approximation – majorization minimization – parallel optimization algorithms – nonconvex optimization – nonsmooth optimization – block coordinate descent – phase retrieval – dictionary learning

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