Related papers: Efficient algorithms for optimal homology problems…

Deep Neural Network (DNN) based super-resolution algorithms have greatly improved the quality of the generated images. However, these algorithms often yield significant artifacts when dealing with real-world super-resolution problems due to…

In this paper, we formulate the Load Flow (LF) problem in radial electricity distribution networks as an unconstrained Riemannian optimization problem, consisting of two manifolds, and we consider alternative retractions and initialization…

Densest Subgraph Problem (DSP) is an important primitive problem with a wide range of applications, including fraud detection, community detection and DNA motif discovery. Edge-based density is one of the most common metrics in DSP.…

The minimum-cost flow (MCF) problem is a fundamental optimization problem with many applications and seems to be well understood. Over the last half century many algorithms have been developed to solve the MCF problem and these algorithms…

An efficient method for solving large nonlinear problems combines Newton solvers and Domain Decomposition Methods (DDM). In the DDM framework, the boundary conditions can be chosen to be primal, dual or mixed. The mixed approach presents…

We design a self size-estimating feed-forward network (SSFN) using a joint optimization approach for estimation of number of layers, number of nodes and learning of weight matrices. The learning algorithm has a low computational complexity,…

Optimal transport (OT) and unbalanced optimal transport (UOT) are central in many machine learning, statistics and engineering applications. 1D OT is easily solved, with complexity O(n log n), but no efficient algorithm was known for 1D…

We introduce the Circular Directional Flow Decomposition (CDFD), a new framework for analyzing circularity in weighted directed networks. CDFD separates flow into two components: a circular (divergence-free) component and an acyclic…

We study how to reduce the reconfiguration time in hybrid optical-electrical Datacenter Networks (DCNs). With a layer of Optical Circuit Switches (OCSes), hybrid optical-electrical DCNs can reconfigure its logical topologies to better match…

We present PFNN, a penalty-free neural network method, to efficiently solve a class of second-order boundary-value problems on complex geometries. To reduce the smoothness requirement, the original problem is reformulated to a weak form so…

Recent years have witnessed a tremendous growth using topological summaries, especially the persistence diagrams (encoding the so-called persistent homology) for analyzing complex shapes. Intuitively, persistent homology maps a potentially…

Recently, a framework considering RNA sequences and their RNA secondary structures as pairs, led to some information-theoretic perspectives on how the semantics encoded in RNA sequences can be inferred. In this context, the pairing arises…

Biological and physical systems often exhibit distinct structures at different spatial/temporal scales. Persistent homology is an algebraic tool that provides a mathematical framework for analyzing the multi-scale structures frequently…

In this paper, we propose distributed solvers for systems of linear equations given by symmetric diagonally dominant M-matrices based on the parallel solver of Spielman and Peng. We propose two versions of the solvers, where in the first,…

We address the problem of configuring a power distribution network with reliability and resilience objectives by satisfying the demands of the consumers and saturating each production source as little as possible. We consider power…

Due to diverse architectures in deep neural networks (DNNs) with severe overparameterization, regularization techniques are critical for finding optimal solutions in the huge hypothesis space. In this paper, we propose an effective…

This paper presents an efficient optimization technique for gridless {2-D} line spectrum estimation, named decoupled atomic norm minimization (D-ANM). The framework of atomic norm minimization (ANM) is considered, which has been…

In Part I of this paper, we proposed and analyzed a novel algorithmic framework for the minimization of a nonconvex (smooth) objective function, subject to nonconvex constraints, based on inner convex approximations. This Part II is devoted…

Ensuring solution feasibility is a key challenge in developing Deep Neural Network (DNN) schemes for solving constrained optimization problems, due to inherent DNN prediction errors. In this paper, we propose a ``preventive learning''…

The hybrid linear modeling problem is to identify a set of d-dimensional affine sets in a D-dimensional Euclidean space. It arises, for example, in object tracking and structure from motion. The hybrid linear model can be considered as the…