Algorithms for approximating minimization problems in Hilbert spaces (Q534233)

The authors investigate the following optimization problem in a real Hilbert space: \[ \mu/2\langle Bx,x\rangle+ 1/2\| x\|^2- h(x)\to \min,\quad\text{subject to }x\in\text{Fix}(S)\cap\Omega, \] where \(B\) is a bounded linear operator, \(\mu\geq 0\), \(h\) is a potential function, \(\text{Fix}(S)\) is the set of fixed points of the nonexpansive mapping \(S\), and \(\Omega\) is a solution set of an equilibrium problem. An explicit and an implicit iterative algorithm for solving this problem are proposed.