Iterative Algorithms And Its Applications For The Minimum-norm Solution Of Constrained Convex Minimization Problem

The constrained convex minimization problem is widely used in signal processing and detection,communication engineering,network engineering,data analysis,economics.The generalized equilibrium problem is widely used in optimization,control theory,game theory,engineering and mechanics.The zero points problem is widely used in physics,economics and engineering.Firstly,the author studies constrained convex minimization problem in Hilbert space.By determining the range of step-size,the author proposes new regularized gradient projection algorithms and obtains strong convergence theorems.The convergence point is the minimum-norm solution of constrained convex minimization problem.Then,the author constructs iterative algorithms to study constrained convex minimization problem and generalized equilibrium problem,obtains strong convergence theorems.Last,the author constructs iterative algorithms to study constrained convex minimization problem and zero points problem,obtains strong convergence theorems.The specific research contents are as follows:Firstly,the author studies constrained convex minimization problem,constructs implicit and explicit regularized gradient projection algorithms,obtains strong convergence theorems and the proofs.Secondly,the author studies constrained convex minimization problem and generalized equilibrium problem,constructs implicit and explicit iterative algorithms to solve the common minimum-norm solution of the two problems,obtains strong convergence theorems and the proofs.Thirdly,the author studies constrained convex minimization problem and zero points problem,constructs implicit and explicit iterative algorithms to solve the common minimum-norm solution of the two problems,obtains strong convergence theorems and the proofs.