Jicheng Li By reviewing the primal-dual hybrid algorithm (PDHA) proposed by He, You and Yuan (SIAM J. Imaging Sci. 2014;7(4):2526-2537), in this paper we introduce four improved schemes for solving a class of generalized saddle-point problems. By making use of the variational inequality, weaker conditions are presented to ensure the global convergence of the proposed algorithms, where … Read more
In the literature, there are a few researches for the proximal point algorithm (PPA) with some parameters in the proximal matrix, especially for the multi-objective optimization problems. Introducing some parameters to the PPA will make it more attractive and flexible. By using the unified framework of the classical PPA and constructing a parameterized proximal matrix, … Read more
In this paper, we develop a Parameterized Proximal Point Algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent with a worst-case $O(1/t)$ convergence rate, where $t$ is the iteration number. By properly choosing the algorithm parameters, numerical experiments … Read more
The Alternating Direction Method of Multipliers (ADMM) has been proved to be effective for solving separable convex optimization subject to linear constraints. In this paper, we propose a Generalized Symmetric ADMM (GS-ADMM), which updates the Lagrange multiplier twice with suitable stepsizes, to solve the multi-block separable convex programming. This GS-ADMM partitions the data into two … Read more