An extrapolated fixed-point optimization method for strongly convex smooth optimizations

Abstract

In this work, we focused on minimizing a strongly convex smooth function over the common fixed-point constraints. We proposed an extrapolated fixed-point optimization method, which is a modified version of the extrapolated sequential constraint method with conjugate gradient direction. We proved the convergence of the generated sequence to the unique solution to the considered problem without boundedness assumption. We also investigated some numerical experiments to underline the effectiveness and performance of the proposed method.

Keywords

• conjugate gradient method
• cutter
• extrapolated method
• strong convergence
• strong convexity