5,289 research outputs found
PRISMA: PRoximal Iterative SMoothing Algorithm
Motivated by learning problems including max-norm regularized matrix
completion and clustering, robust PCA and sparse inverse covariance selection,
we propose a novel optimization algorithm for minimizing a convex objective
which decomposes into three parts: a smooth part, a simple non-smooth Lipschitz
part, and a simple non-smooth non-Lipschitz part. We use a time variant
smoothing strategy that allows us to obtain a guarantee that does not depend on
knowing in advance the total number of iterations nor a bound on the domain
Conic Optimization Theory: Convexification Techniques and Numerical Algorithms
Optimization is at the core of control theory and appears in several areas of
this field, such as optimal control, distributed control, system
identification, robust control, state estimation, model predictive control and
dynamic programming. The recent advances in various topics of modern
optimization have also been revamping the area of machine learning. Motivated
by the crucial role of optimization theory in the design, analysis, control and
operation of real-world systems, this tutorial paper offers a detailed overview
of some major advances in this area, namely conic optimization and its emerging
applications. First, we discuss the importance of conic optimization in
different areas. Then, we explain seminal results on the design of hierarchies
of convex relaxations for a wide range of nonconvex problems. Finally, we study
different numerical algorithms for large-scale conic optimization problems.Comment: 18 page
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