An Iterative Approach to Quadratic Optimization

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Strong Convergence Theorems for a Finite Family of Nonexpansive Mappings (2007, methodology): “In [2], it is proved that the sequence {xn} defined by the iterative method below, with the initial guess x0 ∈H chosen arbitrarily, xn+1 = ( I −αnA ) Sxn +αnb, n≥ 0, (1.”
A General Iterative Method for Equilibrium Problems and Fixed Point Problems in Hilbert Spaces (2008, background): “In [6], it is proved that the sequence {xn} defined by the iterative method below, with the initial guess x0 ∈ H chosen arbitrarily, xn+1 = (I − αnA)Sxn + αnb, n ≥ 0, converges strongly to the unique solution of the minimization problem (1.”
A general iterative method for nonexpansive mappings in Hilbert spaces (2006, methodology): “, [1,4,5,7,8] and the references therein.”
Convergence Analysis of Modified Hybrid Steepest-Descent Methods with Variable Parameters for Variational Inequalities (2007, background): “2 ensures that the sequence {un} generated by (18) converges strongly to the unique solution x̂0 = ÂK,θ(b) of (17).”
VISCOSITY APPROXIMATION METHODS FOR NONEXPANSIVE MAPPINGS (2004, background): “Some more discussions on the hypotheses (H1)–(H3) and applications in optimization of the iterative methods for nonexpansive mappings can be found in Xu [8,9].”
An iterative algorithm for solving fixed point problems, variational inequality problems and mixed equilibrium problems (2009, neutral): “, [1–5,27–30].”