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This paper is aimed at presenting a systematic survey of the existing now different formulations for the problem of projection of the origin of the Euclidean space onto the convex polyhedron (PPOCP). In the present paper, there are…
This paper proposes and analyzes a communication-efficient distributed optimization framework for general nonconvex nonsmooth signal processing and machine learning problems under an asynchronous protocol. At each iteration, worker machines…
A notion of "radially monotone" cut paths is introduced as an effective choice for finding a non-overlapping edge-unfolding of a convex polyhedron. These paths have the property that the two sides of the cut avoid overlap locally as the cut…
This paper considers a conceptual version of a convex optimization algorithm whic is based on replacing a convex optimization problem with the root-finding problem for the approximate sub-differential mapping which is solved by repeated…
We consider the complex cut polytope: the convex hull of Hermitian rank 1 matrices $xx^{\mathrm{H}}$, where the elements of $x \in \mathbb{C}^n$ are $m$th unit roots. These polytopes have applications in ${\text{MAX-3-CUT}}$, digital…
This paper proposes a new large-scale mask-compliant spectral precoder (LS-MSP) for orthogonal frequency division multiplexing systems. In this paper, we first consider a previously proposed mask-compliant spectral precoding scheme that…
This paper introduces an efficient $\mathcal{O}(n)$ compute and memory complexity algorithm for globally optimal path planning on 2D Cartesian grids. Unlike existing marching methods that rely on approximate discretized solutions to the…
Optimal transport is an important tool in machine learning, allowing to capture geometric properties of the data through a linear program on transport polytopes. We present a single-loop optimization algorithm for minimizing general convex…
This paper first proposes an N-block PCPM algorithm to solve N-block convex optimization problems with both linear and nonlinear constraints, with global convergence established. A linear convergence rate under the strong second-order…
This paper reports investigations on the computation of material fronts in multi-fluid models using a Lagrange-Projection approach. Various forms of the Projection step are considered. Particular attention is paid to minimization of…
We suggest a unified spectrally matched optimal grid approach for finite-difference and finite-element approximation of the PML. The new approach allows to combine optimal discrete absorption for both evanescent and propagative waves.
As we look to the next generation of adaptive optics systems, now is the time to develop and explore the technologies that will allow us to image rocky Earth-like planets; wavefront control algorithms are not only a crucial component of…
In this letter, we study distributed optimization, where a network of agents, abstracted as a directed graph, collaborates to minimize the average of locally-known convex functions. Most of the existing approaches over directed graphs are…
A new approach for analyzing waveguide junctions containing conductive cylindrical objects is proposed. The algorithm is based on mode matching technique using local projection functions, which improves the numerical conditioning of the…
One of the tasks in color image processing and computer vision is to recover clean data from partial observations corrupted by noise. To this end, robust quaternion matrix completion (QMC) has recently attracted more attention and shown its…
We develop a new approach to tackle communication constraints in a distributed learning problem with a central server. We propose and analyze a new algorithm that performs bidirectional compression and achieves the same convergence rate as…
This article focuses on numerical efficiency of projection algorithms for solving linear optimization problems. The theoretical foundation for this approach is provided by the basic result that bounded finite dimensional linear optimization…
This paper investigates a new class of non-convex optimization, which provides a unified framework for linear precoding in single/multi-user multiple-input multiple-output (MIMO) channels with arbitrary input distributions. The new…
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…
The onset of transformation optics has opened avenues for designing of a plenitude of applications related to propagation of electromagnetic waves in anisotropic media. In this paper, an algorithm is proposed using a coordinate…