16 citations · 31 across the 14 of their papers we have counts for
15 papers
The SiMPL Method for Multi-Material Topology Optimization
Peter Gangl, Brendan Keith, Dohyun Kim +2
We introduce an efficient and scalable method for density-based multi-material topology optimization, integrating classical mirror descent techniques with point-wise polytopal desi…
Risk-Averse Ensemble Control for Control-Affine Systems
Alessandro Scagliotti, Thomas M. Surowiec
A number of important modern applications in optimal control can be formulated as open loop control problems in which the underlying dynamical systems are subject to random inputs.…
Proximal Galerkin for Phase Field Fracture
Miguel Castillón, Biswajit Khara, Jørgen S. Dokken +3
The phase-field method has emerged as a powerful tool for simulating fracture mechanics, yet it presents significant numerical challenges, particularly regarding the enforcement of…
The latent variable proximal point algorithm for variational problems with inequality constraints
Jørgen S. Dokken, Patrick E. Farrell, Brendan Keith +2
The latent variable proximal point (LVPP) algorithm is a framework for solving infinite-dimensional variational problems with pointwise inequality constraints. The algorithm is a s…
A Simple Introduction to the SiMPL Method for Density-Based Topology Optimization
Dohyun Kim, Boyan Stefanov Lazarov, Thomas M. Surowiec +1
We introduce a novel method for solving density-based topology optimization problems: Sigmoidal Mirror descent with a Projected Latent variable (SiMPL). The SiMPL method (pronounce…
Analysis of the SiMPL method for density-based topology optimization
Brendan Keith, Dohyun Kim, Boyan S. Lazarov +1
We present a rigorous convergence analysis of a new method for density-based topology optimization that provides point-wise bound preserving design updates and faster convergence t…
A Risk Management Perspective on Statistical Estimation and Generalized Variational Inference
Aurya S. Javeed, Drew P. Kouri, Thomas M. Surowiec
Generalized variational inference (GVI) provides an optimization-theoretic framework for statistical estimation that encapsulates many traditional estimation procedures. The typica…
Proximal Galerkin: A structure-preserving finite element method for pointwise bound constraints
Brendan Keith, Thomas M. Surowiec
The proximal Galerkin finite element method is a high-order, low-iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of point-wise…
Optimal Control of the Landau-de Gennes Model of Nematic Liquid Crystals
Thomas M. Surowiec, Shawn W. Walker
We present an analysis and numerical study of an optimal control problem for the Landau-de Gennes (LdG) model of nematic liquid crystals (LCs), which is a crucial component in mode…
Risk-averse optimal control of random elliptic variational inequalities
Amal Alphonse, Caroline Geiersbach, Michael Hintermüller +1
We consider a risk-averse optimal control problem governed by an elliptic variational inequality (VI) subject to random inputs. By deriving KKT-type optimality conditions for a pen…
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…
Optimal Control of the Kirchhoff Equation
Masoumeh Hashemi, Roland Herzog, Thomas M. Surowiec
We consider an optimal control problem for the steady-state Kirchhoff equation, a prototype for nonlocal partial differential equations, different from fractional powers of closed…
Asymptotic Properties of Monte Carlo Methods in Elliptic PDE-Constrained Optimization under Uncertainty
Werner Römisch, Thomas M. Surowiec
Monte Carlo approximations for random linear elliptic PDE constrained optimization problems are studied. We use empirical process theory to obtain best possible mean convergence ra…
Computing multiple solutions of topology optimization problems
Ioannis P. A. Papadopoulos, Patrick E. Farrell, Thomas M. Surowiec
Topology optimization problems often support multiple local minima due to a lack of convexity. Typically, gradient-based techniques combined with continuation in model parameters a…
Deflation for semismooth equations
Patrick E. Farrell, Matteo Croci, Thomas M. Surowiec
Variational inequalities can in general support distinct solutions. In this paper we study an algorithm for computing distinct solutions of a variational inequality, without varyin…