6 citations · 18 across the 14 of their papers we have counts for
14 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,…
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…
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…
Descent Properties of an Anderson Accelerated Gradient Method With Restarting
Wenqing Ouyang, Yang Liu, Andre Milzarek
Anderson Acceleration (AA) is a popular acceleration technique to enhance the convergence of fixed-point iterations. The analysis of AA approaches typically focuses on the converge…
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…
A trust region-type normal map-based semismooth Newton method for nonsmooth nonconvex composite optimization
Wenqing Ouyang, Andre Milzarek
We propose a novel trust region method for solving a class of nonsmooth, nonconvex composite-type optimization problems. The approach embeds inexact semismooth Newton steps for fin…
Nonmonotone Globalization for Anderson Acceleration via Adaptive Regularization
Wenqing Ouyang, Jiong Tao, Andre Milzarek +1
Anderson acceleration (AA) is a popular method for accelerating fixed-point iterations, but may suffer from instability and stagnation. We propose a globalization method for AA to…
A Trust-Region Method For Nonsmooth Nonconvex Optimization
Ziang Chen, Andre Milzarek, Zaiwen Wen
We propose a trust-region type method for a class of nonsmooth nonconvex optimization problems where the objective function is a summation of a (probably nonconvex) smooth function…
A Stochastic Extra-Step Quasi-Newton Method for Nonsmooth Nonconvex Optimization
Minghan Yang, Andre Milzarek, Zaiwen Wen +1
In this paper, a novel stochastic extra-step quasi-Newton method is developed to solve a class of nonsmooth nonconvex composite optimization problems. We assume that the gradient o…
On The Geometric Analysis of A Quartic-quadratic Optimization Problem under A Spherical Constraint
Haixiang Zhang, Andre Milzarek, Zaiwen Wen +1
This paper considers the problem of solving a special quartic-quadratic optimization problem with a single sphere constraint, namely, finding a global and local minimizer of $\frac…
A Stochastic Semismooth Newton Method for Nonsmooth Nonconvex Optimization
Andre Milzarek, Xiantao Xiao, Shicong Cen +2
In this work, we present a globalized stochastic semismooth Newton method for solving stochastic optimization problems involving smooth nonconvex and nonsmooth convex terms in the…
Adaptive Regularized Newton Method for Riemannian Optimization
Jiang Hu, Andre Milzarek, Zaiwen Wen +1
Optimization on Riemannian manifolds widely arises in eigenvalue computation, density functional theory, Bose-Einstein condensates, low rank nearest correlation, image registration…