Related papers: Using non-convex approximations for efficient anal…
When designing optimal controllers for any system, it is often the case that the true state of the system is unknown to the controller, for example due to noisy measurements or partially observable states. Incomplete state information must…
In this work, we examine sampling problems with non-smooth potentials. We propose a novel Markov chain Monte Carlo algorithm for sampling from non-smooth potentials. We provide a non-asymptotical analysis of our algorithm and establish a…
Reachability is the problem of deciding whether there is a path from one vertex to the other in the graph. Standard graph traversal algorithms such as DFS and BFS take linear time to decide reachability however their space complexity is…
We show that several problems of compacting orthogonal graph drawings to use the minimum number of rows, area, length of longest edge or total edge length cannot be approximated better than within a polynomial factor of optimal in…
Many optimization algorithms converge to stationary points. When the underlying problem is nonconvex, they may get trapped at local minimizers and occasionally stagnate near saddle points. We propose the Run-and-Inspect Method, which adds…
This paper proposes a simple yet highly accurate prediction-correction algorithm, SHARP, for unconstrained time-varying optimization problems. Its prediction is based on an extrapolation derived from the Lagrange interpolation of past…
We consider a regularized least squares problem, with regularization by structured sparsity-inducing norms, which extend the usual $\ell_1$ and the group lasso penalty, by allowing the subsets to overlap. Such regularizations lead to…
The notion of approachability in repeated games with vector payoffs was introduced by Blackwell in the 1950s, along with geometric conditions for approachability and corresponding strategies that rely on computing {\em steering directions}…
A well-studied continuous model of graphs considers each edge as a continuous unit-length interval of points. In the problem $\delta$-Tour defined within this model, the objective to find a shortest tour that comes within a distance of…
In this paper, we propose a general graph optimization based framework for localization, which can accommodate different types of measurements with varying measurement time intervals. Special emphasis will be on range-based localization.…
Finding approximate stationary points, i.e., points where the gradient is approximately zero, of non-convex but smooth objective functions $f$ over unrestricted $d$-dimensional domains is one of the most fundamental problems in classical…
The problem of minimizing the sum of nonsmooth, convex objective functions defined on a real Hilbert space over the intersection of fixed point sets of nonexpansive mappings, onto which the projections cannot be efficiently computed, is…
We consider large linear and nonlinear fixed point problems, and solution with proximal algorithms. We show that there is a close connection between two seemingly different types of methods from distinct fields: 1) Proximal iterations for…
We consider the mobile robot path planning problem for a class of recurrent reachability objectives. These objectives are parameterized by the expected time needed to visit one position from another, the expected square of this time, and…
Convex nonsmooth optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, the class of first-order algorithms known as proximal splitting algorithms is particularly adequate: they…
Threshold automata are a formalism for modeling fault-tolerant distributed algorithms. The main feature of threshold automata is the notion of a threshold guard, which allows us to compare the number of received messages with the total…
This paper considers a conceptual version of a convex optimization algorithm whic is based on replacing a convex optimization problem with the root-finding problem for the approximate sub-differential mapping which is solved by repeated…
We consider minimizing a function consisting of a quadratic term and a proximable term which is possibly nonconvex and nonsmooth. This problem is also known as scaled proximal operator. Despite its simple form, existing methods suffer from…
Active set method aims to find the correct active set of the optimal solution and it is a powerful method for solving strictly convex quadratic problem with bound constraints. To guarantee the finite step convergence, the existing active…
Reachability analysis is at the core of many applications, from neural network verification, to safe trajectory planning of uncertain systems. However, this problem is notoriously challenging, and current approaches tend to be either too…