Related papers: A Linear-Time Algorithm for Trust Region Problems
Linear programming relaxations are central to {\sc map} inference in discrete Markov Random Fields. The ability to properly solve the Lagrangian dual is a critical component of such methods. In this paper, we study the benefit of using…
Precision matrices play important roles in many practical applications. Motivated by temporally dependent multivariate data in modern social and scientific studies, we consider the statistical inference of precision matrices for…
We present an algorithm to perform trust-region-based optimization for nonlinear unconstrained problems. The method selectively uses function and gradient evaluations at different floating-point precisions to reduce the overall energy…
A classical approach for solving discrete time nonlinear control on a finite horizon consists in repeatedly minimizing linear quadratic approximations of the original problem around current candidate solutions. While widely popular in many…
The solution of linear non-autonomous ordinary differential equation systems (also known as the time-ordered exponential) is a computationally challenging problem arising in a variety of applications. In this work, we present and study a…
We suggest and compare different methods for the numerical solution of Lyapunov like equations with application to control of Markovian jump linear systems. First, we consider fixed point iterations and associated Krylov subspace…
A gradient-based method is proposed for solving the linear quadratic regulator (LQR) problem for linear systems with nonlinear dependence on time-invariant probabilistic parametric uncertainties. The approach explicitly accounts for model…
We study the problem of estimating the covariance matrix of a high-dimensional distribution when a small constant fraction of the samples can be arbitrarily corrupted. Recent work gave the first polynomial time algorithms for this problem…
A computationally efficient method to solve non-convex programming problems with linear equality constraints is presented. The proposed method is based on a recursively feasible and descending sequential convex programming procedure proven…
In this contribution, we are concerned with parameter optimization problems that are constrained by multiscale PDE state equations. As an efficient numerical solution approach for such problems, we introduce and analyze a new relaxed and…
We consider integer and linear programming problems for which the linear constraints exhibit a (recursive) block-structure: The problem decomposes into independent and efficiently solvable sub-problems if a small number of constraints is…
We present a MATLAB implementation of the symmetric rank-one (SC-SR1) method that solves trust-region. subproblems when a limited-memory symmetric rank-one (L-SR1) matrix is used in place of the true Hessian matrix, which can be used for…
We propose a bundle trust-region algorithm to minimize locally Lipschitz functions which are potentially nonsmooth and nonconvex. We prove global convergence of our method and show by way of an example that the classical convergence…
For solving large-scale non-convex problems, we propose inexact variants of trust region and adaptive cubic regularization methods, which, to increase efficiency, incorporate various approximations. In particular, in addition to approximate…
Let $P$ be a path graph of $n$ vertices embedded in a metric space. We consider the problem of adding a new edge to $P$ so that the radius of the resulting graph is minimized, where any center is constrained to be one of the vertices of…
We study a class of fused lasso problems where the estimated parameters in a sequence are regressed toward their respective observed values (fidelity loss), with $\ell_1$ norm penalty (regularization loss) on the differences between…
In this article, we present a family of numerical approaches to solve high-dimensional linear non-symmetric problems. The principle of these methods is to approximate a function which depends on a large number of variates by a sum of tensor…
Continuous-time quantum walks can be used to solve the spatial search problem, which is an essential component for many quantum algorithms that run quadratically faster than their classical counterpart, in $\mathcal O(\sqrt n)$ time for $n$…
We provide the first nearly-linear time algorithm for approximating $\ell_{q \rightarrow p}$-norms of non-negative matrices, for $q \geq p \geq 1$. Our algorithm returns a $(1-\varepsilon)$-approximation to the matrix norm in time…
Bayesian Optimization (BO) is a popular framework for optimizing black-box functions. Despite its effectiveness, BO is often inefficient for high-dimensional problems due to the exponential growth of the search space, heterogeneity of the…