2023/11/22 by C. He, He, Chuan, Huang, Heng +1 · 3 citations
Engineering · Mathematics · Computer Science · #Sparse and Compressive Sensing Techniques #Advanced Optimization Algorithms Research #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2311.13094
In this paper we consider a nonconvex unconstrained optimization problem minimizing a twice differentiable objective function with Hölder continuous Hessian. Specifically, we first propose a Newton-conjugate gradient (Newton-CG) method for finding an approximate first- and second-order stationary point of this problem, assuming the associated the Hölder parameters are explicitly known. Then we develop a parameter-free Newton-CG method without requiring any prior knowledge of these parameters. To the best of our knowledge, this method is the first parameter-free second-order method achieving the best-known iteration and operation complexity for finding an approximate first- and second-order stationary point of this problem. Finally, we present preliminary numerical results to demonstrate the superior practical performance of our parameter-free Newton-CG method over a well-known regularized Newton method.