Related papers: Optimal map-making with singularities

Inverse optimization, determining parameters of an optimization problem that render a given solution optimal, has received increasing attention in recent years. While significant inverse optimization literature exists for convex…

We introduce an algorithm to solve linear inverse problems regularized with the total (gradient) variation in a gridless manner. Contrary to most existing methods, that produce an approximate solution which is piecewise constant on a fixed…

The main contribution of this paper is a new submap joining based approach for solving large-scale Simultaneous Localization and Mapping (SLAM) problems. Each local submap is independently built using the local information through solving a…

Multi-agent planning (MAP) approaches have been typically conceived for independent or loosely-coupled problems to enhance the benefits of distributed planning between autonomous agents as solving this type of problems require less…

In this article, we discuss formal invariants of singularly-perturbed linear differential systems in neighborhood of turning points and give algorithms which allow their computation. The algorithms proposed are implemented in the computer…

Optimizing a network of maps among a collection of objects/domains (or map synchronization) is a central problem across computer vision and many other relevant fields. Compared to optimizing pairwise maps in isolation, the benefit of map…

This paper deals with the numerical computation of the least singular value of a rectangular matrix $A$ relative to a pair of closed convex cones $(P,Q)$, which is defined as the optimal value of the non-convex optimization problem of…

Deep-learning-based methods for different applications have been shown vulnerable to adversarial examples. These examples make deployment of such models in safety-critical tasks questionable. Use of deep neural networks as inverse problem…

We consider the problem of reconstructing rank-one matrices from random linear measurements, a task that appears in a variety of problems in signal processing, statistics, and machine learning. In this paper, we focus on the Alternating…

We propose a simple subsampling scheme for fast randomized approximate computation of optimal transport distances. This scheme operates on a random subset of the full data and can use any exact algorithm as a black-box back-end, including…

While the theory of operator approximation with any given accuracy is well elaborated, the theory of {best constrained} constructive operator approximation is still not so well developed. Despite increasing demands from applications this…

Considering a 2D matrix of positive and negative numbers, how might one draw a rectangle within it whose contents sum higher than all other rectangles'? This fundamental problem, commonly known the maximum rectangle problem or subwindow…

We propose an efficient algorithm to numerically solve Anderson impurity problems using matrix product states. By introducing a modified chain mapping we obtain significantly lower entanglement, as compared to all previous attempts, while…

We investigate the properties of a class of piecewise-fractional maps arising from the introduction of an invariance under rescaling into convex quadratic maps. The subsequent maps are quasiconvex, and pseudoconvex on specific convex cones;…

This note further addresses the global optimization problem for max-plus linear systems considered in [Automatica 119 (2020) 109104]. Firstly, the operations between infinity elemens and real numbers involved in the formulas of solving…

Difficult, in particular NP-complete, optimization problems are traditionally solved approximately using search heuristics. These are usually slowed down by the rugged landscapes encountered, because local minima arrest the search process.…

In unconstrained maximum a posteriori (MAP) and maximum likelihood estimation, the inverse of minus the merit-function Hessian matrix is an approximation of the estimate covariance matrix. In the Bayesian context of MAP estimation, it is…

This work addresses the problem of vehicle path planning in the presence of obstacles and uncertainties, which is a fundamental problem in robotics. While many path planning algorithms have been proposed for decades, many of them have dealt…

Kernel approximation via nonlinear random feature maps is widely used in speeding up kernel machines. There are two main challenges for the conventional kernel approximation methods. First, before performing kernel approximation, a good…

We consider the solution of systems of linear algebraic equations (SLAEs) with an ill-conditioned or degenerate exact matrix and an approximate right-hand side. An approach to solving such a problem is proposed and justified, which makes it…