Related papers: The shortest lengths and the enclosure method for …

A recently introduced technique of topology sensitivity in method of moments is extended by the possibility of adding degrees-of-freedom (reconstruct) into underlying structure. The algebraic formulation is inversion-free, suitable for…

This article studies the solutions of time-dependent differential inclusions which is motivated by their utility in the modeling of certain physical systems. The differential inclusion is described by a time-dependent set-valued mapping…

Contraction analysis considers the distance between two adjacent trajectories. If this distance is contracting, then trajectories have the same long-term behavior. The main advantage of this analysis is that it is independent of the…

This paper is concerned with the multi-frequency factorization method for imaging the support of a wave-number-dependent source function. It is supposed that the source function is given by the inverse Fourier transform of some…

In this paper, we deal with the inverse problem of the shape reconstruction of cavities and inclusions embedded in a linear elastic isotropic medium from boundary displacement's measurements. For, we consider a constrained minimization…

This work is concerned with an inverse elastic scattering problem of identifying the unknown rigid obstacle embedded in an open space filled with a homogeneous and isotropic elastic medium. A Newton-type iteration method relying on the…

We investigate the problem of balanced embedding of a non-compact complex manifold into an infinite-dimensional projective space. In this paper we prove the existence of such an embedding in a model case. The strategy is by using a gradient…

In this article, we present an approximation algorithm for solving the Weighted Region Problem amidst a set of $ n $ non-overlapping weighted disks in the plane. For a given parameter $ \varepsilon \in (0,1]$, the length of the approximate…

Non-convex methods for linear inverse problems with low-dimensional models have emerged as an alternative to convex techniques. We propose a theoretical framework where both finite dimensional and infinite dimensional linear inverse…

Let $X$ be a set of points in $\mathbb{R}^2$ and $\mathcal{O}$ be a set of geometric objects in $\mathbb{R}^2$, where $|X| + |\mathcal{O}| = n$. We study the problem of computing a minimum subset $\mathcal{O}^* \subseteq \mathcal{O}$ that…

Confidence intervals are a standard technique for analyzing data. When applied to time series, confidence intervals are computed for each time point separately. Alternatively, we can compute confidence bands, where we are required to find…

Let us consider a case where all of the elements in some continuous slices are missing in tensor data. In this case, the nuclear-norm and total variation regularization methods usually fail to recover the missing elements. The key problem…

This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…

In this paper we propose an annealing based framework to incorporate inequality constraints in optimization problems such as facility location, simultaneous facility location with path optimization, and the last mile delivery problem. These…

We develop Cresson's non-differentiable embedding to quantum problems of the calculus of variations and optimal control with time delay. Main results show that the dynamics of non-differentiable Lagrangian and Hamiltonian systems with time…

In this paper, we will present a generalization for a minimization problem from I. Daubechies, M. Defrise, and C. Demol [3]. This generalization is useful for solving many practical problems in which more than one constraint are involved.…

Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from…

Enclosing depth is a recently introduced depth measure which gives a lower bound to many depth measures studied in the literature. So far, enclosing depth has only been studied from a combinatorial perspective. In this work, we give the…

We develop time integration methods in low-rank representation that can adaptively adjust approximation ranks to achieve a prescribed accuracy, while ensuring that these ranks remain proportional to the corresponding best approximation…

This is a review article on the development of the probe and enclosure methods from past to present, focused on their central ideas together with various applications.