Quadratic optimization of fixed points of nonexpansive mappings in hubert space

On variational inclusion and common fixed point problems in Hilbert spaces with applications

“…Iterative methods for nonexpansive mappings have recently been applied to solve convex minimization problems; see, e.g., [2,3,7,10,11,18,19,[23][24][25] and the references therein. A typical problem is to minimize a quadratic function over the set of the fixed points of a nonexpansive mapping on a real Hilbert space H: min x2FðSÞ 1 2 hAx; xi À hðxÞ; ð1:2Þ…”

Hybrid viscosity-like approximation methods for nonexpansive mappings in Hilbert spaces

“…On the other hand, iterative methods for nonexpansive mappings have recently been applied to solve convex minimization problems; see, e.g., [14,15,7,16,8] and the references therein. A typical problem is to minimize a quadratic function over the fixed-point set of a nonexpansive mapping on H:…”

A general iterative method of fixed points for equilibrium problems and optimization problems

“…On the other hand, iteration methods for nonexpansive mappings have recently been applied to solve convex minimization problems; see, e.g., [6][7][8][9][10] and references therein. A typical problem is to minimize a quadratic function over the set of the fixed points of a nonexpansive mapping on a real Hilbert space H:…”