Efficient Techniques for Shape Optimization with Variational Inequalities Using Adjoints
DOI10.1137/19M1257226zbMath1444.49014arXiv1904.08650MaRDI QIDQ3300774
Volker H. Schulz, Daniel Luft, Kathrin Welker
Publication date: 30 July 2020
Published in: SIAM Journal on Optimization (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1904.08650
variational inequalitynumerical methodsshape optimizationobstacle problemadjoint methodssemismooth optimization
Numerical methods involving duality (49M29) Variational inequalities (49J40) Optimization of shapes other than minimal surfaces (49Q10) Numerical methods for variational inequalities and related problems (65K15) PDEs in connection with control and optimization (35Q93) Unilateral problems for linear elliptic equations and variational inequalities with linear elliptic operators (35J86)
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- Variational inequalities and frictional contact problems
- Automated solution of differential equations by the finite element method. The FEniCS book
- Pontryagin's principle in the control of semilinear elliptic variational inequalities
- Optimal control of elliptic variational inequalities
- A fat boundary method for the Poisson problem in a domain with holes
- Shape optimization for interface identification with obstacle problems
- Optimal control of a non-smooth semilinear elliptic equation
- Existence of solutions of a dynamic Signorini's problem with nonlocal friction in viscoelasticity
- Applied functional analysis. Main principles and their applications
- Topological derivatives in shape optimization
- Optimal shape design for systems governed by variational inequalities. I: Existence theory for the elliptic case
- Optimal shape design for systems governed by variational inequalities. II: Existence theory for the evolution case
- Overview of the geometries of shape spaces and diffeomorphism groups
- Shape Optimization for a Class of Semilinear Variational Inequalities with Applications to Damage Models
- Nitsche’s method for general boundary conditions
- Optimal Shape Design Subject to Elliptic Variational Inequalities
- Level set methods for geometric inverse problems in linear elasticity
- Efficient PDE Constrained Shape Optimization Based on Steklov--Poincaré-Type Metrics
- First-Order Optimality Conditions for Elliptic Mathematical Programs with Equilibrium Constraints via Variational Analysis
- Shape Differentiability Under Non-linear PDE Constraints
- An active-set equality constrained Newton solver with feasibility restoration for inverse coefficient problems in elliptic variational inequalities
- Level Set Method for Shape and Topology Optimization of Contact Problems
- Mathematical Programs with Complementarity Constraints in Function Space: C- and Strong Stationarity and a Path-Following Algorithm
- Shape Sensitivity Analysis via Min Max Differentiability
- Semi–Smooth Newton Methods for Variational Inequalities of the First Kind
- Algorithmic Aspects of Multigrid Methods for Optimization in Shape Spaces
- Part IV Parallel algorithms for partial differential equations
- A Unified Discrete–Continuous Sensitivity Analysis Method for Shape Optimization
- Convergence analysis of smoothing methods for optimal control of stationary variational inequalities with control constraints
- Variational inequalities
- Sur la régularité de la solution d'inéquations elliptiques
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