The cubic regularization(CR)algorithm has attracted a lot of attentions in the literature in recent years.We propose a new reformulation of the cubic regularization subproblem.The reformulation is an unconstrained con...The cubic regularization(CR)algorithm has attracted a lot of attentions in the literature in recent years.We propose a new reformulation of the cubic regularization subproblem.The reformulation is an unconstrained convex problem that requires computing the minimum eigenvalue of the Hessian.Then,based on this reformulation,we derive a variant of the(non-adaptive)CR provided a known Lipschitz constant for the Hessian and a variant of adaptive regularization with cubics(ARC).We show that the iteration complexity of our variants matches the best-known bounds for unconstrained minimization algorithms using first-and second-order information.Moreover,we show that the operation complexity of both of our variants also matches the state-of-the-art bounds in the literature.Numerical experiments on test problems from CUTEst collection show that the ARC based on our new subproblem reformulation is comparable to the existing algorithms.展开更多
基金supported in part by the National Natural Foundation of China(Nos.11801087 and 12171100).
文摘The cubic regularization(CR)algorithm has attracted a lot of attentions in the literature in recent years.We propose a new reformulation of the cubic regularization subproblem.The reformulation is an unconstrained convex problem that requires computing the minimum eigenvalue of the Hessian.Then,based on this reformulation,we derive a variant of the(non-adaptive)CR provided a known Lipschitz constant for the Hessian and a variant of adaptive regularization with cubics(ARC).We show that the iteration complexity of our variants matches the best-known bounds for unconstrained minimization algorithms using first-and second-order information.Moreover,we show that the operation complexity of both of our variants also matches the state-of-the-art bounds in the literature.Numerical experiments on test problems from CUTEst collection show that the ARC based on our new subproblem reformulation is comparable to the existing algorithms.
