Computing multiple solutions of topology optimization problems
Topology optimization problems often support multiple local minima due to a lack of
convexity. Typically, gradient-based techniques combined with continuation in model …
convexity. Typically, gradient-based techniques combined with continuation in model …
Risk-neutral PDE-constrained generalized Nash equilibrium problems
DB Gahururu, M Hintermüller, TM Surowiec - Mathematical Programming, 2023 - Springer
A class of risk-neutral generalized Nash equilibrium problems is introduced in which the
feasible strategy set of each player is subject to a common linear elliptic partial differential …
feasible strategy set of each player is subject to a common linear elliptic partial differential …
A Generalized -Convergence Concept for a Class of Equilibrium Problems
M Hintermüller, SM Stengl - Journal of Nonlinear Science, 2024 - Springer
A novel generalization of Γ-convergence applicable to a class of equilibrium problems is
studied. After the introduction of the latter, a variety of its applications is discussed. The …
studied. After the introduction of the latter, a variety of its applications is discussed. The …
Deflation for semismooth equations
Variational inequalities can in general support distinct solutions. In this paper we study an
algorithm for computing distinct solutions of a variational inequality, without varying the initial …
algorithm for computing distinct solutions of a variational inequality, without varying the initial …
Proximal Galerkin: A structure-preserving finite element method for pointwise bound constraints
B Keith, TM Surowiec - arXiv preprint arXiv:2307.12444, 2023 - arxiv.org
The proximal Galerkin finite element method is a high-order, nonlinear numerical method
that preserves the geometric and algebraic structure of bound constraints in infinite …
that preserves the geometric and algebraic structure of bound constraints in infinite …
Optimal control of the stationary Kirchhoff equation
M Hashemi, R Herzog, TM Surowiec - Computational Optimization and …, 2023 - Springer
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 …
for nonlocal partial differential equations, different from fractional powers of closed …
A Globalized Inexact Semismooth Newton Method for Nonsmooth Fixed-point Equations involving Variational Inequalities
We develop a semismooth Newton framework for the numerical solution of fixed-point
equations that are posed in Banach spaces. The framework is motivated by applications in …
equations that are posed in Banach spaces. The framework is motivated by applications in …
Projections onto the canonical simplex with additional linear inequalities
We consider the distributionally robust optimization and show that computing the
distributional worst-case is equivalent to computing the projection onto the canonical …
distributional worst-case is equivalent to computing the projection onto the canonical …
Optimization of a multiphysics problem in semiconductor laser design
A multimaterial topology optimization framework using phase fields is suggested for the
simultaneous optimization of mechanical and optical properties to be used in the …
simultaneous optimization of mechanical and optical properties to be used in the …
Optimal Control of Nonlocal Partial Differential Equations
S Hashemibarmchi - 2024 - archiv.ub.uni-heidelberg.de
In the past decades, the optimal control of partial differential equations governed by partial
differential equations has made significant progress. This work concerns optimal control of …
differential equations has made significant progress. This work concerns optimal control of …