Related papers: Robust Least-Squares Optimization for Data-Driven …
This paper presents a methodology for solving a geometrically robust least squares problem, which arises in various applications where the model is subject to geometric constraints. The problem is formulated as a minimax optimization…
In this correspondence, we introduce a minimax regret criteria to the least squares problems with bounded data uncertainties and solve it using semi-definite programming. We investigate a robust minimax least squares approach that minimizes…
This paper discusses robustness guarantees for online tracking of time-varying subspaces from noisy data. Building on recent work in optimization over a Grassmannian manifold, we introduce a new approach for robust subspace tracking by…
Least squares estimation, a regression technique based on minimisation of residuals, has been invaluable in bringing the best fit solutions to parameters in science and engineering. However, in dynamic environments such as in Geomatics…
This paper considers robust solutions to a class of nonlinear least squares problems using min-max optimization approach. We give an explicit formula for the value function of the inner maximization problem and show the existence of global…
We study the problem of estimating an unknown deterministic signal that is observed through an unknown deterministic data matrix under additive noise. In particular, we present a minimax optimization framework to the least squares problems,…
In this paper we formulate and solve a robust least squares problem for a system of linear equations subject to quantization error in the data matrix. Ordinary least squares fails to consider uncertainty in the operator, modeling all noise…
We address the challenge of dimension reduction in the discrete-time optimal control problem which is solved repeatedly online within the framework of model predictive control. Our study demonstrates that a reduced-order approach, aimed at…
We propose a novel approach for navigating in polygonal environments by synthesizing controllers that take as input relative displacement measurements with respect to a set of landmarks. Our algorithm is based on solving a sequence of…
We provide a framework for the numerical approximation of distributed optimal control problems, based on least-squares finite element methods. Our proposed method simultaneously solves the state and adjoint equations and is $\inf$--$\sup$…
We propose a robust and scalable procedure for general optimization and inference problems on manifolds leveraging the classical idea of `median-of-means' estimation. This is motivated by ubiquitous examples and applications in modern data…
We address the problem of fitting parametric curves on the Grassmann manifold for the purpose of intrinsic parametric regression. As customary in the literature, we start from the energy minimization formulation of linear least-squares in…
Studying structural properties of linear dynamical systems through invariant subspaces is one of the key contributions of the geometric approach to system theory. In general, a model of the dynamics is required in order to compute the…
As the scale of problems and data used for experimental design, signal processing and data assimilation grow, the oft-occuring least squares subproblems are correspondingly growing in size. As the scale of these least squares problems…
This paper presents a new approach to solve linear and nonlinear model predictive control (MPC) problems that requires small memory footprint and throughput and is particularly suitable when the model and/or controller parameters change at…
We propose a Binary Robust Least Squares (BRLS) model that encompasses key robust least squares formulations, such as those involving uncertain binary labels and adversarial noise constrained within a hypercube. We show that the geometric…
Practical application of H[infinity] robust control relies on system identification of a valid model-set, described by a linear system in feedback with a stable norm-bounded uncertainty, which must explains all possible (or at least all…
Randomized matrix compression techniques, such as the Johnson-Lindenstrauss transform, have emerged as an effective and practical way for solving large-scale problems efficiently. With a focus on computational efficiency, however, forsaking…
We investigate robust optimization problems defined for maximizing convex functions. For finite uncertainty set, we develop a geometric branch-and-bound algorithmic approach to solve this problem. The geometric branch-and-bound algorithm…
Parameter estimation by nonlinear least squares minimization is a common problem with an elegant geometric interpretation: the possible parameter values of a model induce a manifold in the space of data predictions. The minimization problem…