Related papers: A Discretize-Then-Optimize Approach to PDE-Constra…
The isometric embedding of surfaces in three-dimensional space is fundamental to various physical systems, from elastic sheets to programmable materials. While continuous surfaces typically admit unique solutions under suitable boundary…
This work extends our previous study from S. Shrestha et al. (2024) by introducing a new abstract framework for Variational Multiscale (VMS) methods at the discrete level. We introduce the concept of what we define as the optimal projector…
This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic…
This paper presents a new progressive compression method for triangular meshes. This method, in fact, is based on a schema of irregular multi-resolution analysis and is centered on the optimization of the rate-distortion trade-off. The…
This article proposes a new discrete framework for approximating solutions to shape optimization problems under convexity constraints. The numerical method, based on the support function or the gauge function, is guaranteed to generate…
Shape optimization with constraints given by partial differential equations (PDE) is a highly developed field of optimization theory. The elegant adjoint formalism allows to compute shape gradients at the computational cost of a further PDE…
A new exact projective penalty method is proposed for the equivalent reduction of constrained optimization problems to nonsmooth unconstrained ones. In the method, the original objective function is extended to infeasible points by summing…
Recent progress in PDE constrained optimization on shape manifolds is based on the Hadamard form of shape derivatives, i.e., in the form of integrals at the boundary of the shape under investigation, as well as on intrinsic shape metrics.…
Bayesian optimization works effectively optimizing parameters in black-box problems. However, this method did not work for high-dimensional parameters in limited trials. Parameters can be efficiently explored by nonlinearly embedding them…
We consider shape optimization problems with internal inclusion constraints, of the form $$\min\big\{J(\Omega)\ :\ \Dr\subset\Omega\subset\R^d,\ |\Omega|=m\big\},$$ where the set $\Dr$ is fixed, possibly unbounded, and $J$ depends on…
We consider a class of nonsmooth optimization problems over the Stiefel manifold, in which the objective function is weakly convex in the ambient Euclidean space. Such problems are ubiquitous in engineering applications but still largely…
The accuracy of finite element solutions is closely tied to the mesh quality. In particular, geometrically nonlinear problems involving large and strongly localized deformations often result in prohibitively large element distortions. In…
We introduce an efficient and scalable method for density-based multi-material topology optimization, integrating classical mirror descent techniques with point-wise polytopal design constraints. Such constraints arise naturally in this…
This paper explores a fully discrete approximation for a nonlinear hyperbolic PDE-constrained optimization problem (P) with applications in acoustic full waveform inversion. The optimization problem is primarily complicated by the…
This paper is concerned with finite element error estimates for Neumann boundary control problems posed on convex and polyhedral domains. Different discretization concepts are considered and for each optimal discretization error estimates…
We consider an elliptic optimal control problem where the objective functional contains an integral along a surface of codimension 1, also known as a hypersurface. In particular, we use a fidelity term that encourages the state to take…
We consider the problem of optimization of cost functionals on the infinite-dimensional manifold of diffeomorphisms. We present a new class of optimization methods, valid for any optimization problem setup on the space of diffeomorphisms by…
We introduce a novel formulation for curvature regularization by penalizing normal curvatures from multiple directions. This total normal curvature regularization is capable of producing solutions with sharp edges and precise isotropic…
We consider shape optimization problems involving functionals depending on perimeter, torsional rigidity and Lebesgue measure. The scaling free cost functionals are of the form $P(\Omega)T^q(\Omega)|\Omega|^{-2q-1/2}$ and the class of…
We present a general numerical approach to shape optimization with state constraints for 2-dimensional geometries, without relaxing the constraints. To do this we reformulate the problem on a fixed reference domain using a conformal…