Department of Mathematics
Customized proximal point algorithms for linearly constrained convex minimization and saddle-point problems: A unified approach
This paper focuses on some customized applications of the proximal point algorithm (PPA) to two classes of problems: the convex minimization problem with linear constraints and a generic or separable objective function, and a saddle-point problem. We treat these two classes of problems uniformly by a mixed variational inequality, and show how the application of PPA with customized metric proximal parameters can yield favorable algorithms which are able to make use of the models' structures effectively. Our customized PPA revisit turns out to unify some algorithms including some existing ones in the literature and some new ones to be proposed. From the PPA perspective, we establish the global convergence and a worst-case O(1/t) convergence rate for this series of algorithms in a unified way. © 2013 Springer Science+Business Media New York.
Convergence rate, Convex minimization, Customized algorithms, Proximal point algorithm, Saddle-point problem, Splitting algorithms
Source Publication Title
Computational Optimization and Applications
Link to Publisher's Edition
Gu, G., He, B., & Yuan, X. (2014). Customized proximal point algorithms for linearly constrained convex minimization and saddle-point problems: A unified approach. Computational Optimization and Applications, 59 (2-1), 135-161. https://doi.org/10.1007/s10589-013-9616-x