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Consider a polyhedral convex cone which is given by a finite number of linear inequalities. We investigate the problem to project this cone into a subspace and show that this problem is closely related to linear vector optimization: We…
The Kaczmarz method is an iterative numerical method for solving large and sparse rectangular systems of linear equations. Gearhart, Koshy and Tam have developed an acceleration technique for the Kaczmarz method that minimizes the distance…
A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…
In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…
When solving linear systems $Ax=b$, $A$ and $b$ are given, but the measurements $b$ often contain corruptions. Inspired by recent work on the quantile-randomized Kaczmarz method, we propose an acceleration of the randomized Kaczmarz method…
In this paper, we propose a probabilistic reduced-dimensional vector autoregressive (PredVAR) model with oblique projections. This model partitions the measurement space into a dynamic subspace and a static subspace that do not need to be…
This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorithm, we prove a contraction estimate that…
The multi-step inertial randomized Kaczmarz (MIRK) method is an iterative method for solving large-scale linear systems. In this paper, we enhance the MIRK method by incorporating the greedy probability criterion, coupled with the…
We propose a distributed positioning algorithm to estimate the unknown positions of a number of target nodes, given distance measurements between target nodes and between target nodes and a number of reference nodes at known positions.…
The Kaczmarz method is successfully used for solving discretizations of linear inverse problems, especially in computed tomography where it is known as ART. Practitioners often observe and appreciate its fast convergence in the first few…
We present a method for solving the general mixed constrained convex quadratic programming problem using an active set method on the dual problem. The approach is similar to existing active set methods, but we present a new way of solving…
We construct a convergent family of outer approximations for the problem of optimizing polynomial functions over convex bodies subject to polynomial constraints. This is achieved by generalizing the polarization hierarchy, which has…
Phase retrieval has been an attractive but difficult problem rising from physical science, and there has been a gap between state-of-the-art theoretical convergence analyses and the corresponding efficient retrieval methods. Firstly, these…
A new algorithm for deciding the satisfiability of polynomial formulas over the reals is proposed. The key point of the algorithm is a new projection operator, called sample-cell projection operator, custom-made for Conflict-Driven Clause…
Motivated by the need for decentralized learning, this paper aims at designing a distributed algorithm for solving nonconvex problems with general linear constraints over a multi-agent network. In the considered problem, each agent owns…
Two optimization algorithms are proposed for solving a stochastic programming problem for which the objective function is given in the form of the expectation of convex functions and the constraint set is defined by the intersection of…
We introduce sparse random projection, an important dimension-reduction tool from machine learning, for the estimation of discrete-choice models with high-dimensional choice sets. Initially, high-dimensional data are compressed into a…
Nowadays, the field computed tomography (CT) encompasses a large variety of settings, ranging from nanoscale to meter-sized objects imaged by different kinds of radiation in various acquisition modes. This experimental diversity challenges…
With nowadays steadily growing quantum processors, it is required to develop new quantum tomography tools that are tailored for high-dimensional systems. In this work, we describe such a computational tool, based on recent ideas from…
A Graph of Convex Sets (GCS) is a graph in which vertices are associated with convex programs and edges couple pairs of programs through additional convex costs and constraints. Any optimization problem over an ordinary weighted graph…