The split feasibility problem (SFP), which provides a unified framework to model a wide range of inverse problems, has received much considerable attention in the literature.However, how to efficiently solve SFPs is still an interesting topic.In this paper, we introduce a block-wise formulation for algorithmic design.Specifically, we first introduce an auxiliary variable to formulate the original SFP as a constrained minimization problem with a block structure, which paves a new way to find solutions of SFPs.Then, we show that the employments of some classical gradient-type optimization algorithms produce very simple, yet quite efficient iterative schemes to find a solution of SFPs when the underlying block structure could be exploited.The parallel iterative schemes of the proposed blockwise algorithms are not only efficient to deal with the case that the projections onto the convex sets have explicit representations, but also are possibly valuable for solving large-scale SFPs without explicit projections onto the underlying sets.Some numerical results on synthetic examples support the idea of this paper.
We study a new class of variational inclusion problems in the framework of real Hilbert spaces.We propose two Tseng-type algorithms with inertial extrapolation for solving these problems and carry out the convergence analysis of these two methods.We also give an application of our results to solve convex bilevel optimization problems.
In this paper, we propose three self-adaptive relaxed CQ-algorithms with projections onto halfspaces for solving a split equality problem.The stepsize of the algorithms is dynamically calculated without any prior information regarding operator norms.Moreover, we prove the strong convergence to the minimum-norm solution of the split equality problem.Finally, we test the validity of our results by conducting some numerical experiments and consider signal recovery problems as applications.
In this paper, we propose a hybrid Halpern-based extragradient algorithm for finding a common solution of a pseudomonotone equilibrium problem and a fixed point problem of a nonexpansive mapping.We prove the strong convergence of the proposed algorithm under some mixed conditions.Some numerical examples are provided to illustrate the effectiveness of the proposed algorithm.
Entropy-regularized quadratic optimization problems are a special class of optimization problems with wide applications in various fields, such as transportation and machine learning.In this paper, we apply the augmented Lagrangian method to this problem with its subproblem solved by the block coordinate descent method.Under certain mild conditions, we analyze the global convergence of this algorithm.Numerical experiments demonstrate the effectiveness of this algorithm.
