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math.OC2022
Analysis of the primal-dual central path for nonlinear semidefinite optimization without the nondegeneracy condition
Takayuki Okuno
We study properties of the central path underlying a nonlinear semidefinite optimization problem, called NSDP for short. The latest radical work on this topic was contributed by Ya…
math.OC2022
Riemannian Levenberg-Marquardt Method with Global and Local Convergence Properties
Sho Adachi, Takayuki Okuno, Akiko Takeda
We extend the Levenberg-Marquardt method on Euclidean spaces to Riemannian manifolds. Although a Riemannian Levenberg-Marquardt (RLM) method was produced by Peeters in 1993, to the…
math.OC2022★ 1 cited
Accelerated-gradient-based generalized Levenberg--Marquardt method with oracle complexity bound and local quadratic convergence
Naoki Marumo, Takayuki Okuno, Akiko Takeda
Minimizing the sum of a convex function and a composite function appears in various fields. The generalized Levenberg--Marquardt (LM) method, also known as the prox-linear method,…