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Riemannian optimization is a principled framework for solving optimization problems where the desired optimum is constrained to a smooth manifold $\mathcal{M}$. Algorithms designed in this framework usually require some geometrical…
We propose and study an algorithm for computing a nearest passive system to a given non-passive linear time-invariant system (with much freedom in the choice of the metric defining `nearest', which may be restricted to structured…
The skeleton of a digital image is a compact representation of its topology, geometry, and scale. It has utility in many computer vision applications, such as image description, segmentation, and registration. However, skeletonization has…
Variational Quantum algorithms, especially Quantum Approximate Optimization and Variational Quantum Eigensolver (VQE) have established their potential to provide computational advantage in the realm of combinatorial optimization. However,…
We present a new accelerated gradient-based method for solving smooth unconstrained optimization problems. The goal is to embed a heavy-ball type of momentum into the Fast Gradient Method (FGM). For this purpose, we devise a generalization…
Deformations of the computational mesh arising from optimization routines usually lead to decrease of mesh quality or even destruction of the mesh. We propose a theoretical framework using pre-shapes to generalize classical shape…
This book is about solving matrix nearness problems that are related to eigenvalues or singular values or pseudospectra. These problems arise in great diversity in various fields, be they related to dynamics, as in questions of robust…
We propose a novel numerical algorithm for computing the electronic structure related eigenvalue problem of incommensurate systems. Unlike the conventional practice that approximates the system by a large commensurate supercell, our…
Iterative multiscale methods for electronic structure calculations offer several advantages for large-scale problems. Here we examine a nonlinear full approximation scheme (FAS) multigrid method for solving fixed potential and…
An efficient computational approach for imaging binary-type physical properties suitable for various models in biomedical applications is developed and validated. The proposed methodology includes gradient-based multiscale optimization with…
This paper proposes a new gradient-based optimization approach for designing optimal feedback kernels for parabolic distributed parameter systems with boundary control. Unlike traditional kernel optimization methods for parabolic systems,…
Computational meshes arising from shape optimization routines commonly suffer from decrease of mesh quality or even destruction of the mesh. In this work, we provide an approach to regularize general shape optimization problems to increase…
Optimization and control of complex unsteady flows remains an important challenge due to the large cost of performing a function evaluation, i.e. a full computational fluid dynamics (CFD) simulation. Reducing the number of required function…
Realizing high-throughput aberration-corrected Scanning Transmission Electron Microscopy (STEM) exploration of atomic structures requires rapid tuning of multipole probe correctors while compensating for the inevitable drift of the optical…
In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape…
An important step in shape optimization with partial differential equation constraints is to adapt the geometry during each optimization iteration. Common strategies are to employ mesh-deformation or re-meshing, where one or the other…
This work develops an algorithm for PDE-constrained shape optimization based on Lipschitz transformations. Building on previous work in this field, the $p$-Laplace operator is utilized to approximate a descent method for Lipschitz shapes.…
This paper focuses on minimizing a smooth function combined with a nonsmooth regularization term on a compact Riemannian submanifold embedded in the Euclidean space under a decentralized setting. Typically, there are two types of approaches…
The solution of (generalized) eigenvalue problems for symmetric or Hermitian matrices is a common subtask of many numerical calculations in electronic structure theory or materials science. Solving the eigenvalue problem can easily amount…
Shape optimization based on shape calculus has received a lot of attention in recent years, particularly regarding the development, analysis, and modification of efficient optimization algorithms. In this paper we propose and investigate…