Related papers: Gabor frame bound optimizations
We design accelerated algorithms with improved rates for several fundamental classes of optimization problems. Our algorithms all build upon techniques related to the analysis of primal-dual extragradient methods via relative Lipschitzness…
A broad class of optimization problems can be cast in composite form, that is, considering the minimization of the composition of a lower semicontinuous function with a differentiable mapping. This paper investigates the versatile template…
By applying a recently proposed mapping, we derive exactly the upper phase boundary of several Ising spin glass models defined over static graphs and random graphs, generalizing some known results and providing new ones.
We study the combinatorics of hyperplane arrangements over arbitrary fields. Specifically, we determine in which situation an arrangement and its reduction modulo a prime number have isomorphic lattices via the use of minimal strong…
We give an optimal upper bound for the maximum-norm distance from a vertex of a knapsack polyhedron to its nearest feasible lattice point. In a randomised setting, we show that the upper bound can be significantly improved on average. As a…
Atoms deeply trapped in magic wavelength optical lattices provide a Doppler- and collision-free dense ensemble of quantum emitters ideal for high precision spectroscopy. Thus, they are the basis of some of the best optical clock setups to…
In this contribution I discuss a recent proposal of a novel action for lattice gauge theory for finite systems, which accommodates non-periodic spatial boundary conditions. Drawing on the summation-by-parts formulation of finite differences…
In this paper, the problem of finding optimal success probabilities of static linear optics quantum gates is linked to the theory of convex optimization. It is shown that by exploiting this link, upper bounds for the success probability of…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…
We study computational and statistical consequences of problem geometry in stochastic and online optimization. By focusing on constraint set and gradient geometry, we characterize the problem families for which stochastic- and…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
An important yet challenging problem in numerical linear algebra is finding a principal submatrix with maximum determinant from a given symmetric positive semidefinite matrix. This problem arises in experimental design, statistics, and…
We investigate the optimal selection of weight windows for the problem of weighted least squares. We show that weight windows should be symmetric around its center, which is also its peak. We consider the class of tapered rectangle window…
The article focuses on the problems of prime gaps and zero spacings. Possible solutions of several related problems such as the greatest lower bound, the least upper bound of the zero spacings, and the least upper bound of the prime gaps…
We develop a theory of quantum harmonic analysis on lattices in $\mathbb{R}^{2d}$. Convolutions of a sequence with an operator and of two operators are defined over a lattice, and using corresponding Fourier transforms of sequences and…
In this paper, we study superlinear systems that give rise to free boundaries. Such systems appear for example from the minimization of the energy functional $$ \int_{\Omega}\left(|\nabla\mathbf{u}|^2+\frac2p|\mathbf{u}|^p\right),\quad…
Numerical integration over the real line for analytic functions is studied. Our main focus is on the sharpness of the error bounds. We first derive two general lower estimates for the worst-case integration error, and then apply these to…
We consider Hamiltonian deformations of Gabor systems, where the window evolves according to the action of a Schr\"odinger propagator and the phase-space nodes evolve according to the corresponding Hamiltonian flow. We prove the stability…
A numerical study of an optimal control formulation for a shape optimization problem governed by an elliptic variational inequality is performed. The shape optimization problem is reformulated as a boundary control problem in a fixed…
A Gabor system in $L^2(\mathbb{R})$, generated by a window $g\in L^2(\mathbb{R})$ and associated with a sequence of times and frequencies $\Gamma\subset\mathbb{R}^2$, is a set formed by translations in time and modulations of $g$. In this…