Related papers: The Nearest Graph Laplacian in Frobenius Norm
This paper proposes a stochastic gradient descent method with an adaptive Gaussian noise term for the global minimization of nearly convex functions, which are nonconvex and possess multiple strict local minimizers. The noise term,…
We present a general method of designing fast approximation algorithms for cut-based minimization problems in undirected graphs. In particular, we develop a technique that given any such problem that can be approximated quickly on trees,…
Given a directed graph of nodes and edges connecting them, a common problem is to find the shortest path between any two nodes. Here we show that the shortest path distances can be found by a simple matrix inversion: If the edges are given…
The radius and diameter are fundamental graph parameters. They are defined as the minimum and maximum of the eccentricities in a graph, respectively, where the eccentricity of a vertex is the largest distance from the vertex to another…
Graph sparsification underlies a large number of algorithms, ranging from approximation algorithms for cut problems to solvers for linear systems in the graph Laplacian. In its strongest form, "spectral sparsification" reduces the number of…
This paper deals with a Tikhonov regularized second-order inertial dynamical system that incorporates time scaling, asymptotically vanishing damping and Hessian-driven damping for solving convex optimization problems. Under appropriate…
In the past two decades, the field of applied finance has tremendously benefited from graph theory. As a result, novel methods ranging from asset network estimation to hierarchical asset selection and portfolio allocation are now part of…
A novel inner approximation algorithm is proposed for dynamic optimization problems to ensure strict satisfaction of path constraints. Distinct from traditional methods relying on interval analysis, the proposed algorithm leverages the…
The graph similarity problem, also known as approximate graph isomorphism or graph matching problem, has been extensively studied in the machine learning community, but has not received much attention in the algorithms community: Given two…
The Max-Cut problem is a fundamental NP-hard problem, which is attracting attention in the field of quantum computation these days. Regarding the approximation algorithm of the Max-Cut problem, algorithms based on semidefinite programming…
We present a new feasible proximal gradient method for constrained optimization where both the objective and constraint functions are given by the summation of a smooth, possibly nonconvex function and a convex simple function. The…
Given a matrix $A$, a matrix nearness problem seeks an $X$ that most closely approximates $A$ in the sense of minimizing $\lVert A - X\rVert$ under a variety of constraints on $X$. A generalized matrix nearness problem seeks the same but…
This work provides closed-form solutions and minimum achievable errors for a large class of low-rank approximation problems in Hilbert spaces. The proposed theorem generalizes to the case of bounded linear operators the previous results…
This work deals with the generation of theoretical correlation matrices with specific sparsity patterns, associated to graph structures. We present a novel approach based on convex optimization, offering greater flexibility compared to…
We consider the problem of analyzing and designing gradient-based discrete-time optimization algorithms for a class of unconstrained optimization problems having strongly convex objective functions with Lipschitz continuous gradient. By…
We study subset selection for matrices defined as follows: given a matrix $\matX \in \R^{n \times m}$ ($m > n$) and an oversampling parameter $k$ ($n \le k \le m$), select a subset of $k$ columns from $\matX$ such that the pseudo-inverse of…
For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…
This paper considers the fixed point problem for a nonexpansive mapping on a real Hilbert space and proposes novel line search fixed point algorithms to accelerate the search. The termination conditions for the line search are based on the…
Given a graph $G=(V,E)$ with two distinguished vertices $s,t\in V$ and an integer parameter $L>0$, an {\em $L$-bounded cut} is a subset $F$ of edges (vertices) such that the every path between $s$ and $t$ in $G\setminus F$ has length more…
We develop a family of accelerated stochastic algorithms that minimize sums of convex functions. Our algorithms improve upon the fastest running time for empirical risk minimization (ERM), and in particular linear least-squares regression,…