The Research On Iterative Algorithms Of Split Feasibility Problems And Related Problems

The split feasibility problem is an important problem in optimization theory,and many complex physical processes are described by the split feasibility problem.For example,signal processing,image reconstruction,and radiation therapy,etc.This thesis aims to study the split feasibility problem and related problems in the real Hilbert space.The following contents are investigated in this thesis:1.Moudafi proposed an approximate splitting algorithm and an alternating CQ algorithm for solving the split feasibility problem and the split equality problem,respectively.In the approximate splitting algorithm,the step size sequence 9)is implicit,and only weak convergence results are obtained for these two algorithms.This thesis introduces a viscosity term and combines inertial techniques to propose two projection algorithms that strongly converge,respectively,to solve the split feasibility problem and the split equality problem.2.This thesis transforms the split feasibility problem with multiple output sets into the fixed point problem with multiple output sets,and proposes a strongly convergent projection algorithm to solve the fixed point problem with multiple output sets.The equilibrium problem and the fixed point problem with multiple output sets are combined,and a new projection algorithm is constructed to find their common solution.3.This thesis proposes a strongly convergent relaxed alternating CQ algorithm for solving split equality problems.The algorithm constructs a half-space and uses the projection onto the half-space instead of the projection onto a closed convex set in the adaptive iterative algorithm,which reduces the computation of the projection.