Related papers: Finding the nearest passive or non-passive system …
We consider the problem of selectively controlling couplings in a practical quantum processor with always-on interactions that are diagonal in the computational basis, using sequences of local NOT gates. This methodology is well-known in…
The focus in this paper is interior-point methods for bound-constrained nonlinear optimization, where the system of nonlinear equations that arise are solved with Newton's method. There is a trade-off between solving Newton systems…
In this paper, we consider the problem of computing the nearest stable matrix to an unstable one. We propose new algorithms to solve this problem based on a reformulation using linear dissipative Hamiltonian systems: we show that a matrix…
Rank deficient Hankel matrices are at the core of several applications. However, in practice, the coefficients of these matrices are noisy due to e.g. measurements errors and computational errors, so generically the involved matrices are…
We consider the uniform approximation of the smallest eigenvalue of a large parameter-dependent Hermitian matrix by that of a smaller counterpart obtained through projections. The projection subspaces are constructed iteratively by means of…
Given a structured matrix $A$ we study the problem of finding the closest normal matrix with the same structure. The structures of our interest are: Hamiltonian, skew-Hamiltonian, per-Hermitian, and perskew-Hermitian. We develop a…
We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on the eigenvector, or several eigenvectors (or their corresponding invariant subspace). The algorithms are derived from an implicit…
Many applications require solving non-linear control problems that are classically not well behaved. This paper develops a simple and efficient chattering algorithm that learns near optimal decision policies through an open-loop feedback…
We consider the problem of computing the nearest matrix polynomial with a non-trivial Smith Normal Form. We show that computing the Smith form of a matrix polynomial is amenable to numeric computation as an optimization problem.…
Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The…
A Hamiltonian algorithm, both theoretical and numerical, to obtain the reduced equations implementing Pontryagine's Maximum Principle for singular linear-quadratic optimal control problems is presented. This algorithm is inspired on the…
Large-scale eigenvalue problems pose a significant challenge to classical computers. While there are efficient quantum algorithms for unitary or Hermitian matrices, eigenvalue problems for non-normal matrices remain open in quantum…
Rational filter functions can be used to improve convergence of contour-based eigensolvers, a popular family of algorithms for the solution of the interior eigenvalue problem. We present a framework for the optimization of rational filters…
In this paper, we propose an interior-point method for linearly constrained optimization problems (possibly nonconvex). The method - which we call the Hessian barrier algorithm (HBA) - combines a forward Euler discretization of Hessian…
Many applications in machine learning or signal processing involve nonsmooth optimization problems. This nonsmoothness brings a low-dimensional structure to the optimal solutions. In this paper, we propose a randomized proximal gradient…
Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the…
Manipulating Hamiltonians governing physical systems has found a broad range of applications, from quantum chemistry to semiconductor design. In this work, we provide a new way of manipulating Hamiltonians, by transforming their eigenvalues…
Structured optimization problems are ubiquitous in fields like data science and engineering. The goal in structured optimization is using a prescribed set of points, called atoms, to build up a solution that minimizes or maximizes a given…
Recently, significant connections between compressed sensing problems and optimization of a particular class of functions relating to solutions of Hamilton-Jacobi equation was discovered. In this paper we introduce a fast approximate…
This paper presents a method for computing eigenvalues and eigenvectors for some types of nonlinear eigenvalue problems. The main idea is to approximate the functions involved in the eigenvalue problem by rational functions and then apply a…