5 papers · 1 filter
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,…
Variational Properties of Decomposable Functions. Part I: Strict Epi-Calculus and Applications
Wenqing Ouyang, Andre Milzarek
This work provides a systematic study of the variational properties of decomposable functions which are compositions of an outer support function and an inner smooth mapping under…
A Semismooth Newton Stochastic Proximal Point Algorithm with Variance Reduction
Andre Milzarek, Fabian Schaipp, Michael Ulbrich
We develop an implementable stochastic proximal point (SPP) method for a class of weakly convex, composite optimization problems. The proposed stochastic proximal point algorithm i…