Abstract
In this paper, we consider a bilevel optimization problem as a task of finding the optimum of the upper-level problem subject to the solution set of the split feasibility problem of fixed point problems and optimization problems. Based on proximal and gradient methods, we propose a strongly convergent iterative algorithm with an inertia effect solving the bilevel optimization problem under our consideration. Furthermore, we present a numerical example of our algorithm to illustrate its applicability.
Highlights
IntroductionLet H be a real Hilbert space and consider the constrained minimization problem: min h s.t. x ∈ C (1)
Let H be a real Hilbert space and consider the constrained minimization problem: min h s.t. x ∈ C (1)where C is a nonempty closed convex subset of H and h : H → R is a convex and continuously differentiable function
Lopez et al [14] introduced a new way of selecting the step sizes that the information of operator norm is not necessary for solving a split feasibility problem (SFP): find x ∈ C such that Ax ∈ Q
Summary
Let H be a real Hilbert space and consider the constrained minimization problem: min h s.t. x ∈ C (1). In the early study of the iterative method of solving the split feasibility problem [11,12,13], the determination of the step-size depends on the operator norm (or at least estimate value of the operator norm) and this is not as easy of a task To overcome this difficulty, Lopez et al [14] introduced a new way of selecting the step sizes that the information of operator norm is not necessary for solving a split feasibility problem (SFP): find x ∈ C such that Ax ∈ Q where C and Q are closed convex subsets of real Hilbert spaces H1 and H2, respectively. We introduce a proximal gradient inertial algorithm with a strong convergence result for approximating a bilevel optimization problem (7), where our algorithm is designed to address a way of selecting the step-sizes such that its implementation does not need any prior information about the operator norm
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
