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20212026
most citedSample Average Approximations of Strongly Convex Stochastic Programs in Hilbert Spaces

13 citations · 29 across the 9 of their papers we have counts for

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11 papers

math.OC2026

A Feasible-Direction-Type Method for Nonconvex Optimization with Infeasible Starts

Danlin Li, Johannes Milz

We develop an infeasible-start extension of the Topkis--Veinott feasible-direction method for nonconvex composite optimization. At each main iteration, a strongly convex local mode…

math.OC2026

Optimal Spectral Design with Prior Information

Anton J. Kleywegt, Johannes Milz, Mohit Singh +1

We study a class of spectral design problems in which a prior positive semidefinite information matrix is updated by a sum of rank-one matrices constructed from chosen design vecto…

math.OC2025

Sample-Based Consistency in Infinite-Dimensional Conic-Constrained Stochastic Optimization

Caroline Geiersbach, Johannes Milz

This paper is concerned with a class of stochastic optimization problems defined on a Banach space with almost sure conic-type constraints. For this class of problems, we investiga…

math.OC2024

Empirical risk minimization for risk-neutral composite optimal control with applications to bang-bang control

Johannes Milz, Daniel Walter

Nonsmooth composite optimization problems under uncertainty are prevalent in various scientific and engineering applications. We consider risk-neutral composite optimal control pro…

math.OC2024

Criticality measure-based error estimates for infinite dimensional optimization

Danlin Li, Johannes Milz

Motivated by optimization with differential equations, we consider optimization problems with Hilbert spaces as decision spaces. As a consequence of their infinite dimensionality,…

math.OC2023

Consistency of sample-based stationary points for infinite-dimensional stochastic optimization

Johannes Milz

We consider stochastic optimization problems with possibly nonsmooth integrands posed in Banach spaces and approximate these stochastic programs via a sample-based approaches. We e…

math.OC2022★ 3 cited

Asymptotic Consistency for Nonconvex Risk-Averse Stochastic Optimization with Infinite Dimensional Decision Spaces

Johannes Milz, Thomas M. Surowiec

Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it…

math.OC2022★ 4 cited

Sample Size Estimates for Risk-Neutral Semilinear PDE-Constrained Optimization

Johannes Milz, Michael Ulbrich

The sample average approximation (SAA) approach is applied to risk-neutral optimization problems governed by semilinear elliptic partial differential equations with random inputs.…

math.OC2022★ 4 cited

Reliable Error Estimates for Optimal Control of Linear Elliptic PDEs with Random Inputs

Johannes Milz

We discretize a risk-neutral optimal control problem governed by a linear elliptic partial differential equation with random inputs using a Monte Carlo sample-based approximation a…

math.OC2022★ 5 cited

Consistency of Monte Carlo Estimators for Risk-Neutral PDE-Constrained Optimization

Johannes Milz

We apply the sample average approximation (SAA) method to risk-neutral optimization problems governed by nonlinear partial differential equations (PDEs) with random inputs. We anal…

math.OC2021★ 13 cited

Sample Average Approximations of Strongly Convex Stochastic Programs in Hilbert Spaces

Johannes Milz

We analyze the tail behavior of solutions to sample average approximations (SAAs) of stochastic programs posed in Hilbert spaces. We require that the integrand be strongly convex w…