Related papers: On joint eigen-decomposition of matrices
The submodular partitioning problem asks to minimize, over all partitions $P$ of a ground set $V$, the sum of a given submodular function $f$ over the parts of $P$. The problem has seen considerable work in approximability, as it…
We consider mappings, which are structure consisting of a single function (and possibly some number of unary relations) and address the problem of approximating a continuous mapping by a finite mapping. This problem is the inverse problem…
A new method to represent and approximate rotation matrices is introduced. The method represents approximations of a rotation matrix $Q$ with linearithmic complexity, i.e. with $\frac{1}{2}n\lg(n)$ rotations over pairs of coordinates,…
Conventional ways to solve optimization problems on low-rank matrix sets which appear in great number of applications ignore its underlying structure of an algebraic variety and existence of singular points. This leads to appearance of…
Many problems of theoretical and practical interest involve finding an optimum over a family of convex functions. For instance, finding the projection on the convex functions in $H^k(\Omega)$, and optimizing functionals arising from some…
This paper considers a distributed optimization problem over a multi-agent network, in which the objective function is a sum of individual cost functions at the agents. We focus on the case when communication between the agents is described…
This book is about solving matrix nearness problems that are related to eigenvalues or singular values or pseudospectra. These problems arise in great diversity in various fields, be they related to dynamics, as in questions of robust…
We study the question of the existence of a dual extremal function for a bounded matrix function on the unit circle in connection with the problem of approximation by analytic matrix functions. We characterize the class of matrix functions,…
A broad range of inverse problems can be abstracted into the problem of minimizing the sum of several convex functions in a Hilbert space. We propose a proximal decomposition algorithm for solving this problem with an arbitrary number of…
In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…
Matrices arising in scientific applications frequently admit linear low-rank approximations due to smoothness in the physical and/or temporal domain of the problem. In large-scale problems, computing an optimal low-rank approximation can be…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…
We consider the minimization or maximization of the $J$th largest eigenvalue of an analytic and Hermitian matrix-valued function, and build on Mengi et al. (2014, SIAM J. Matrix Anal. Appl., 35, 699-724). This work addresses the setting…
Diagonalization, or eigenvalue decomposition, is very useful in many areas of applied mathematics, including signal processing and quantum physics. Matrix decomposition is also a useful tool for approximating matrices as the product of a…
The maximum (or minimum) generalized eigenvalue of symmetric positive semidefinite matrices that depend on optimization variables often appears as objective or constraint functions in structural topology optimization when we consider…
Given a matrix $A$, a matrix nearness problem seeks an $X$ that most closely approximates $A$ in the sense of minimizing $\lVert A - X\rVert$ under a variety of constraints on $X$. A generalized matrix nearness problem seeks the same but…
We study the convergence of a family of numerical integration methods where the numerical integral is formulated as a finite matrix approximation to a multiplication operator. For bounded functions, the convergence has already been…
The multiplication of matrices is an important arithmetic operation in computational mathematics. In the context of hierarchical matrices, this operation can be realized by the multiplication of structured block-wise low-rank matrices,…
The purpose of this paper is to introduce two new classes of accelerated distributed proximal conjugate gradient algorithms for multi-agent constrained optimization problems; given as minimization of a function decomposed as a sum of M…
We present a new algorithm for solving a polynomial program P based on the recent "joint + marginal" approach of the first author for, parametric optimization. The idea is to first consider the variable x1 as a parameter and solve the…