4 papers
A linesearch-type normal map-based semismooth Newton method for nonsmooth nonconvex composite optimization
Hanfeng Zeng, Wenqing Ouyang, Andre Milzarek
We propose a novel linesearch variant of the trust region normal map-based semismooth Newton method developed in [Ouyang and Milzarek, Math. Program. 212(1-2), 389--435 (2025)] for…
A MINRES-based Linesearch Algorithm for Nonconvex Optimization with Non-positive Curvature Detection
Hanfeng Zeng, Yang Liu, Wenqing Ouyang +1
We propose a MINRES-based Newton-type algorithm for solving unconstrained nonconvex optimization problems. Our approach uses the minimal residual method (MINRES), a well-known solv…
Variational Properties of Decomposable Functions. Part II: Strong Second-Order Theory
Wenqing Ouyang, Andre Milzarek
Local superlinear convergence of the semismooth Newton method usually necessitates assumptions on the uniform invertibility of the utilized, generalized Jacobian matrices, such as,…
Obtaining Pseudo-inverse Solutions With MINRES
Yang Liu, Andre Milzarek, Fred Roosta
The celebrated minimum residual method (MINRES), proposed in the seminal paper of Paige and Saunders, has seen great success and widespread use in solving Hermitian (and complex-sy…