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Solving the inverse kinematics problem is a fundamental challenge in motion planning, control, and calibration for articulated robots. Kinematic models for these robots are typically parametrized by joint angles, generating a complicated…
This paper focuses on recovering a low-rank tensor from its incomplete measurements. We propose a novel algorithm termed the Single Mode Quasi Riemannian Gradient Descent (SM-QRGD). By exploiting the benefits of both fixed-rank matrix…
We study a type of Riemannian gradient descent (RGD) algorithm, designed through Riemannian preconditioning, for optimization on $\mathcal{M}_k^{m\times n}$ -- the set of $m\times n$ real matrices with a fixed rank $k$. Our analysis is…
The paper studies a geometrically robust least-squares problem that extends classical and norm-based robust formulations. Rather than minimizing residual error for fixed or perturbed data, we interpret least-squares as enforcing approximate…
This paper is concerned with low-rank matrix optimization, which has found a wide range of applications in machine learning. This problem in the special case of matrix sensing has been studied extensively through the notion of Restricted…
In this paper, we study a general low-rank matrix recovery problem with linear measurements corrupted by some noise. The objective is to understand under what conditions on the restricted isometry property (RIP) of the problem local search…
Recovering high-resolution images from limited sensory data typically leads to a serious ill-posed inverse problem, demanding inversion algorithms that effectively capture the prior information. Learning a good inverse mapping from training…
Understanding how systems built out of modular components can be jointly optimized is an important problem in biology, engineering, and machine learning. The backpropagation algorithm is one such solution and has been instrumental in the…
We study the Inexact Restoration framework with random models for minimizing functions whose evaluation is subject to errors. We propose a constrained formulation that includes well-known stochastic problems and an algorithm applicable when…
We propose an extremely versatile approach to address a large family of matrix nearness problems, possibly with additional linear constraints. Our method is based on splitting a matrix nearness problem into two nested optimization problems,…
This paper studies stability and symmetry preserving $H^2$ optimal model reduction problems of linear systems which include linear gradient systems as a special case. The problem is formulated as a nonlinear optimization problem on the…
Many machine learning and data science tasks require solving non-convex optimization problems. When the loss function is a sum of multiple terms, a popular method is the stochastic gradient descent. Viewed as a process for sampling the loss…
The article introduces a new algorithm for solving a class ofequilibrium problems involving strongly pseudomonotone bifunctions with Lipschitz-type condition. We describe how to incorporate the proximal-like regularized technique with…
We consider Riemannian inequality-constrained optimization problems. Such problems inherit the benefits of Riemannian approach developed in the unconstrained setting and naturally arise from applications in control, machine learning, and…
Modern technologies are producing datasets with complex intrinsic structures, and they can be naturally represented as matrices instead of vectors. To preserve the latent data structures during processing, modern regression approaches…
We study optimization of finite sums of geodesically smooth functions on Riemannian manifolds. Although variance reduction techniques for optimizing finite-sums have witnessed tremendous attention in the recent years, existing work is…
This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…
We give robust recovery results for synchronization on the rotation group, $\mathrm{SO}(D)$. In particular, we consider an adversarial corruption setting, where a limited percentage of the observations are arbitrarily corrupted. We give a…
In the remote state estimation problem, an observer tries to reconstruct the state of a dynamical system at a remote location, where no direct sensor measurements are available. The observer only has access to information sent through a…
A class of recovering algorithms for 1-bit compressive sensing (CS) named Soft Consistency Reconstructions (SCRs) are proposed. Recognizing that CS recovery is essentially an optimization problem, we endeavor to improve the characteristics…