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Optimizing smooth convex functions in stochastic settings, where only noisy estimates of gradients and Hessians are available, is a fundamental problem in optimization. While first-order methods possess a low per-iteration cost, their…
Motivated by TRACE algorithm [Curtis et al. 2017], we propose a trust region algorithm for finding second order stationary points of a linearly constrained non-convex optimization problem. We show the convergence of the proposed algorithm…
We develop several new communication-efficient second-order methods for distributed optimization. Our first method, NEWTON-STAR, is a variant of Newton's method from which it inherits its fast local quadratic rate. However, unlike Newton's…
This study proposes a Newton based multiple objective optimization algorithm for hyperparameter search. The first order differential (gradient) is calculated using finite difference method and a gradient matrix with vectorization is formed…
Time-frequency analysis, such as the Gabor transform, plays an important role in many signal processing applications. The redundancy of such representations is often directly related to the computational load of any algorithm operating in…
We show that the method of factorizing the evolution operator to fourth order with purely positive coefficients, in conjunction with Suzuki's method of implementing time-ordering of operators, produces a new class of powerful algorithms for…
Two-point zeroth order methods are important in many applications of zeroth-order optimization, such as robotics, wind farms, power systems, online optimization, and adversarial robustness to black-box attacks in deep neural networks, where…
Finding an $\epsilon$-stationary point of a nonconvex function with a Lipschitz continuous Hessian is a central problem in optimization. Regularized Newton methods are a classical tool and have been studied extensively, yet they still face…
We describe an algorithm for the application of the forward and inverse spherical harmonic transforms. It is based on a new method for rapidly computing the forward and inverse associated Legendre transforms by hierarchically applying the…
Projected gradient descent and its Riemannian variant belong to a typical class of methods for low-rank matrix estimation. This paper proposes a new Nesterov's Accelerated Riemannian Gradient algorithm by efficient orthographic retraction…
We derive new equations using the mixed-frame approach for one- and two-dimensional (axisymmetric) time-dependent radiation transport and the associated couplings with matter. Our formulation is multi-group and multi-angle and includes…
We study approximate distributed solutions to the weighted {\it all-pairs-shortest-paths} (APSP) problem in the CONGEST model. We obtain the following results. $1.$ A deterministic $(1+o(1))$-approximation to APSP in $\tilde{O}(n)$ rounds.…
For many shape analysis problems in computer vision and scientific imaging (e.g., computational anatomy, morphological cytometry), the ability to align two closed curves in the plane is crucial. In this paper, we concentrate on rigidly…
Estimating ego-pose from cameras is an important problem in robotics with applications ranging from mobile robotics to augmented reality. While SOTA models are becoming increasingly accurate, they can still be unwieldy due to high…
We exhibit a randomized algorithm which given a matrix $A\in \mathbb{C}^{n\times n}$ with $\|A\|\le 1$ and $\delta>0$, computes with high probability an invertible $V$ and diagonal $D$ such that $\|A-VDV^{-1}\|\le \delta$ using…
Nonnegative matrix factorization (NMF) is a popular method for audio spectral unmixing. While NMF is traditionally applied to off-the-shelf time-frequency representations based on the short-time Fourier or Cosine transforms, the ability to…
We present a numerical method to solve the optimal transport problem with a quadratic cost when the source and target measures are periodic probability densities. This method is based on a numerical resolution of the corresponding…
We introduce a new event shape observable -- event isotropy -- that quantifies how close the radiation pattern of a collider event is to a uniform distribution. This observable is based on a normalized version of the energy mover's…
In this paper, we investigate the problem of estimating the 4-DOF (three-dimensional position and orientation) robot-robot relative frame transformation using odometers and distance measurements between robots. Firstly, we apply a two-step…
In this work we deal with parametric inverse problems, which consist in recovering a finite number of parameters describing the structure of an unknown object, from indirect measurements. State-of-the-art methods for approximating a…