Related papers: A fixed-point algorithm for matrix projections wit…
This tutorial introduces a systematic approach for addressing the key question of quantum metrology: For a generic task of sensing an unknown parameter, what is the ultimate precision given a constrained set of admissible strategies. The…
In this paper, we establish sublinear and linear convergence of fixed point iterations generated by averaged operators in a Hilbert space. Our results are achieved under a bounded H\"older regularity assumption which generalizes the…
This paper develops a fixed-point iteration to solve the steady-state water flow equations in an urban water distribution network. The fixed-point iteration is derived upon the assumption of turbulent flow solutions and the validity of the…
We propose a strategy for the generation of fast and accurate versions of non-commutative recursive matrix multiplication algorithms. To generate these algorithms, we consider matrix and tensor norm bounds governing the stability and…
Variational inference is an approximation framework for Bayesian inference that seeks to improve quantified uncertainty in predictions by optimizing a simplified distribution over parameters to stand in for the full posterior. Capturing…
We present a hybrid algorithm for optimizing a convex, smooth function over the cone of positive semidefinite matrices. Our algorithm converges to the global optimal solution and can be used to solve general large-scale semidefinite…
We consider a general class of regression models with normally distributed covariates, and the associated nonconvex problem of fitting these models from data. We develop a general recipe for analyzing the convergence of iterative algorithms…
We propose an SQP algorithm for mathematical programs with vanishing constraints which solves at each iteration a quadratic program with linear vanishing constraints. The algorithm is based on the newly developed concept of $\mathcal…
B\'ezier simplex fitting algorithms have been recently proposed to approximate the Pareto set/front of multi-objective continuous optimization problems. These new methods have shown to be successful at approximating various shapes of Pareto…
This study presents novel methods for computing fixed points of positive concave mappings and for characterizing the existence of fixed points. These methods are particularly important in planning and optimization tasks in wireless…
The Halpern algorithm is a powerful fixed point approximation method for finding the closest point in the fixed point set of a nonexpansive mapping to the initial point. However, in practice, it is not necessarily true that this algorithm…
In this paper, we develop a parameterized proximal point algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent…
We show that an idea, originating initially with a fundamental recursive iteration scheme (usually referred as "the" Kaczmarz algorithm), admits important applications in such infinite-dimensional, and non-commutative, settings as are…
The circumcentered-reflection method (CRM) has been recently proposed as a methodology for accelerating several algorithms for solving the Convex Feasibility Problem (CFP), equivalent to finding a common fixed-point of the orthogonal…
In this article a unified approach to iterative soft-thresholding algorithms for the solution of linear operator equations in infinite dimensional Hilbert spaces is presented. We formulate the algorithm in the framework of generalized…
We present new algorithms for $M$-estimators of multivariate scatter and location and for symmetrized $M$-estimators of multivariate scatter. The new algorithms are considerably faster than currently used fixed-point and related algorithms.…
We consider applications involving a large set of instances of projecting points to polytopes. We develop an intuition guided by theoretical and empirical analysis to show that when these instances follow certain structures, a large…
We present some accelerated variants of fixed point iterations for computing the minimal non-negative solution of the unilateral matrix equation associated with an M/G/1-type Markov chain. These variants derive from certain staircase…
We derive a new variational principle for the quantum Fisher information leading to a simple iterative alternating algorithm, the convergence of which is proved. The case of a fixed measurement, i.e. the classical Fisher information, is…
Computational imaging has been revolutionized by compressed sensing algorithms, which offer guaranteed uniqueness, convergence, and stability properties. Model-based deep learning methods that combine imaging physics with learned…