Distance Geometry is based on the inverse problem that asks to find the positions of points, in a Euclidean space of given dimension, that are compatible with a given set of distances. We briefly introduce the field, and discuss some open and promising research areas. Article Download View Open research areas in distance geometry
In this paper, we consider a class of optimization problems with orthogonality constraints, the feasible region of which is called the Stiefel manifold. Our new framework combines a function value reduction step with a correction step. Different from the existing approaches, the function value reduction step of our algorithmic framework searches along the standard Euclidean … Read more
The max-$k$-sum of a set of real scalars is the maximum sum of a subset of size $k$, or alternatively the sum of the $k$ largest elements. We study two extensions: First, we show how to obtain smooth approximations to functions that are pointwise max-$k$-sums of smooth functions. Second, we discuss how the max-$k$-sum can … Read more
Abstract Absolute positioning magnetic rulers are rulers which calculate the distance of the reading head based just on one reading of a magnetic signal. A new absolute positioning magnetic ruler method which is based on rulers with trapezoidal magnetic poles is considered in this paper. On a fixed position of a ruler, the reading head … Read more
The l0-minimization problem that seeks the sparsest point of a polyhedral set is a longstanding challenging problem in the fields of signal and image processing, numerical linear algebra and mathematical optimization. The weighted l1-method is one of the most plausible methods for solving this problem. In this paper, we develop a new weighted l1-method through … Read more
An unconditionally energy stable time stepping scheme is introduced to solve Cahn-Morral-like equations in the present study. It is constructed based on the combination of David Eyre’s time stepping scheme and Schur complement approach. Although the presented method is general and independent to the choice of homogeneous free energy density function term, logarithmic and polynomial … Read more
The ensemble density functional theory is valuable for simulations of metallic systems due to the absence of a gap in the spectrum of the Hamiltonian matrices. Although the widely used self-consistent field iteration method can be extended to solve the minimization of the total energy functional with respect to orthogonality constraints, there is no theoretical … Read more
In this paper, we propose a new step size rule to accelerate Yan et al.’s self-adaptive projection method. Under the new step size strategy, the superiority of modified projection method is verified through theory to numerical experiments. Citation College of Communications Engineering, PLA University of Science and Technology, Nanjing, 210007, China 01/29/2015 Article Download View … Read more
In this paper we propose a new way to compute a warm starting point for a challenging global optimization problem related to Earth imaging in geophysics. The warm start consists of a velocity model that approximately solves a full-waveform inverse problem at low frequency. Our motivation arises from the availability of massively parallel computing platforms … Read more
The study of matrix inequalities in a dimension-free setting is in the realm of free real algebraic geometry (RAG). In this paper we investigate constrained trace and eigenvalue optimization of noncommutative polynomials. We present Lasserre’s relaxation scheme for trace optimization based on semidefinite programming (SDP) and demonstrate its convergence properties. Finite convergence of this relaxation … Read more