Related papers: Nonlinear bang-bang eigenproblems and optimization…
Roughly speaking, a near-best (abbr. NB) quasi-interpolant (abbr. QI) is an approximation operator of the form $Q_af=\sum_{\alpha\in A} \Lambda_\alpha (f) B_\alpha$ where the $B_\alpha$'s are B-splines and the $\Lambda_\alpha (f)$'s are…
We use Pontryagin's minimum principle to optimize variational quantum algorithms. We show that for a fixed computation time, the optimal evolution has a bang-bang (square pulse) form, both for closed and open quantum systems with Markovian…
In this paper we study the fundamental problems of maximizing a continuous non-monotone submodular function over the hypercube, both with and without coordinate-wise concavity. This family of optimization problems has several applications…
We study the eigenvalue problem for the Dirichlet Laplacian in bounded simply connected plane domains $\Omega\subset\mathbb{C}$ using conformal transformations of the original problem to the weighted eigenvalue problem for the Dirichlet…
We consider two-point non-self-adjoint boundary eigenvalue problems for linear matrix differential operators. The coefficient matrices in the differential expressions and the matrix boundary conditions are assumed to depend analytically on…
We study the sample complexity of differentially private optimization of quasi-concave functions. For a fixed input domain $\mathcal{X}$, Cohen et al. (STOC 2023) proved that any generic private optimizer for low sensitive quasi-concave…
This paper considers robust solutions to a class of nonlinear least squares problems using min-max optimization approach. We give an explicit formula for the value function of the inner maximization problem and show the existence of global…
Local solutions for variational and quasi-variational inequalities are usually the best type of solutions that could practically be obtained when in case of lack of convexity or else when available numerical techniques are too limited for…
In this paper, we propose an unconstrained framework for eigenvalue problems in both discrete and continuous settings. We begin our discussion to solve a generalized eigenvalue problem $A{\bf x} = \lambda B{\bf x}$ with two $N\times N$ real…
We consider the following eigenvalue optimization in the composite membrane problem with fractional Laplacian: given a bounded domain $\Omega\subset \mathbb{R}^n$, $\alpha>0$ and $0<A<|\Omega|$, find a subset $D\subset \Omega$ of area $A$…
In this paper, we propose to analyze stable and unstable modes of generic image denoisers through nonlinear eigenvalue analysis. We attempt to find input images for which the output of a black-box denoiser is proportional to the input. We…
Nonlinear eigenvalue problems for pairs of homogeneous convex functions are particular nonlinear constrained optimization problems that arise in a variety of settings, including graph mining, machine learning, and network science. By…
Low-rank pseudoinverses are widely used to approximate matrix inverses in scalable machine learning, optimization, and scientific computing. However, real-world matrices are often observed with noise, arising from sampling, sketching, and…
Let $T : \Omega \rightarrow \bbC^{n \times n}$ be a matrix-valued function that is analytic on some simply-connected domain $\Omega \subset \bbC$. A point $\lambda \in \Omega$ is an eigenvalue if the matrix $T(\lambda)$ is singular. In this…
Recently, Ferrulli-Laptev-Safronov (2016arXiv161205304F) obtained eigenvalue estimates for an operator associated to bilayer graphene in terms of $L^q$ norms of the (possibly non-selfadjoint) potential. They proved that for $1<q<4/3$ all…
We revisit the computation of quasinormal modes (QNMs) of the Kerr black hole using a numerical approach exploiting a representation of the Teukolsky equation as a $2D$ elliptic partial differential equation. By combining the hyperboloidal…
We complete the study concerning the minimization of the positive principal eigenvalue associated with a weighted Neumann problem settled in a bounded regular domain $\Omega\subset \mathbb{R}^{N}$, $N\ge2$, for the weight varying in a…
We discuss the recent advances in meta-optics and nanophotonics associated with the physics of bound states in the continuum (BICs). Such resonant states appear due to a strong coupling between leaky modes in optical guiding structures…
In this article we study the quasi-linear equation \[ \left\{ \begin{aligned} \mathrm{div}\, \mathcal A(x,u,\nabla u)&=\mathcal B(x,u,\nabla u)&&\text{in }\Omega,\\ u\in H^{1,p}_{loc}&(\Omega;wdx) \end{aligned} \right. \] where $\mathcal A$…
We use exact enumeration to characterize the solutions of quadratic unconstrained binary optimization problems of less than 21 variables in terms of their distributions of Hamming distances to close-by solutions. We also perform experiments…