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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]