Related papers: A deterministic sublinear-time nonadaptive algorit…
For every fixed constant $\alpha > 0$, we design an algorithm for computing the $k$-sparse Walsh-Hadamard transform of an $N$-dimensional vector $x \in \mathbb{R}^N$ in time $k^{1+\alpha} (\log N)^{O(1)}$. Specifically, the algorithm is…
In this paper, we devise three deterministic algorithms for solving the $m$-set $k$-packing, $m$-dimensional $k$-matching, and $t$-dominating set problems in time $O^*(5.44^{mk})$, $O^*(5.44^{(m-1)k})$ and $O^*(5.44^{t})$, respectively.…
We analyse the convergence of an approximate, fully inexact, ADMM algorithm under additive, deterministic and probabilistic error models. We consider the generalized ADMM scheme that is derived from generalized Lagrangian penalty with…
An algorithm for unconstrained non-convex optimization is described, which does not evaluate the objective function and in which minimization is carried out, at each iteration, within a randomly selected subspace. It is shown that this…
In this technical note, a recursive set-membership filtering algorithm for discrete-time nonlinear dynamical systems subject to unknown but bounded process and measurement noises is proposed. The nonlinear dynamics is represented in a…
We study the sublinear multivariate mean estimation problem in $d$-dimensional Euclidean space. Specifically, we aim to find the mean $\mu$ of a ground point set $A$, which minimizes the sum of squared Euclidean distances of the points in…
The analysis of randomized search heuristics on classes of functions is fundamental for the understanding of the underlying stochastic process and the development of suitable proof techniques. Recently, remarkable progress has been made in…
We study the problem of opportunistic approachability: a generalization of Blackwell approachability where the learner would like to obtain stronger guarantees (i.e., approach a smaller set) when their adversary limits themselves to a…
We consider the Partition problem and propose a deterministic FPTAS (Fully Polynomial-Time Approximation Scheme) that runs in $\widetilde{O}(n + 1/\varepsilon)$-time. This is the best possible (up to a polylogarithmic factor) assuming the…
We propose an unconstrained optimization method based on the well-known primal-dual hybrid gradient (PDHG) algorithm. We first formulate the optimality condition of the unconstrained optimization problem as a saddle point problem. We then…
Motivated by reduction of computational complexity, this work develops sign-error adaptive filtering algorithms for estimating time-varying system parameters. Different from the previous work on sign-error algorithms, the parameters are…
In this paper, we propose a variable metric method for unconstrained multiobjective optimization problems (MOPs). First, a sequence of points is generated using different positive definite matrices in the generic framework. It is proved…
We study sublinear time algorithms for estimating the size of maximum matching in graphs. Our main result is a $(\frac{1}{2}+\Omega(1))$-approximation algorithm which can be implemented in $O(n^{1+\epsilon})$ time, where $n$ is the number…
We discuss non-Euclidean deterministic and stochastic algorithms for optimization problems with strongly and uniformly convex objectives. We provide accuracy bounds for the performance of these algorithms and design methods which are…
For many nonlinear Bayesian state estimation problems, the posterior recursion is not analytically tractable, leading to algorithms that are influenced by numerical approximation errors. These algorithms depend on parameters that affect the…
For any two-dimensional nearest neighbor shift of finite type X and any integer n > 0, one can define the horizontal strip shift H_n(X) to be the set of configurations on Z x {1,...,n} which do not contain any forbidden transitions for X.…
Given an unconditionally stable algorithm for solving the Cahn-Hilliard equation, we present a general calculation for an analytic time step $\d \tau$ in terms of an algorithmic time step $\dt$. By studying the accumulative multi-step error…
Adaptive Moment Estimation (ADAM) is a very popular training algorithm for deep neural networks and belongs to the family of adaptive gradient descent optimizers. However to the best of the authors knowledge no complete convergence analysis…
The Monotone Min-Plus Product problem is a useful primitive that has seen many algorithmic applications over the past decade. In this problem, we are given two $n\times n$ integer matrices $A$ and $B$, where each row of $B$ is a monotone…
We consider the classical $k$-Center problem in undirected graphs. The problem is known to have a polynomial-time 2-approximation. There are even $(2+\varepsilon)$-approximations running in near-linear time. The conventional wisdom is that…