Related papers: Maximum vanishing subspace problem, CAT(0)-space r…
We consider the following Scr\"odinger system $$\begin{cases}\displaystyle i\partial_t u + \Delta u +(|u|^2+\beta |v|^2) u= 0, \\ \displaystyle i\partial_t v + \Delta v +(|v|^2+\beta |u|^2) v = 0,\end{cases}$$ with initial data $(u_0,v_0)…
The class $(r,2)$-CSP, or simply Max 2-CSP, consists of constraint satisfaction problems with at most two $r$-valued variables per clause. For instances with $n$ variables and $m$ binary clauses, we present an $O(n r^{5+19m/100})$-time…
A majorized accelerated block coordinate descent (mABCD) method in Hilbert space is analyzed to solve a sparse PDE-constrained optimization problem via its dual. The finite element approximation method is investigated. The attractive…
In this paper, we consider a well-known sparse optimization problem that aims to find a sparse solution of a possibly noisy underdetermined system of linear equations. Mathematically, it can be modeled in a unified manner by minimizing…
In this paper, we study the nearest stable matrix pair problem: given a square matrix pair $(E,A)$, minimize the Frobenius norm of $(\Delta_E,\Delta_A)$ such that $(E+\Delta_E,A+\Delta_A)$ is a stable matrix pair. We propose a reformulation…
This work extends our previous study from S. Shrestha et al. (2024) by introducing a new abstract framework for Variational Multiscale (VMS) methods at the discrete level. We introduce the concept of what we define as the optimal projector…
We present an algorithm for recovering planted solutions in two well-known models, the stochastic block model and planted constraint satisfaction problems, via a common generalization in terms of random bipartite graphs. Our algorithm…
The partition of a problem into smaller sub-problems satisfying certain properties is often a key ingredient in the design of divide-and-conquer algorithms. For questions related to location, the partition problem can be modeled, in…
We advocate a new approach of addressing hidden structure problems and finding efficient quantum algorithms. We introduce and investigate the Hidden Symmetry Subgroup Problem (HSSP), which is a generalization of the well-studied Hidden…
A hierarchy of semidefinite programming (SDP) relaxations approximates the global optimum of polynomial optimization problems of noncommuting variables. Generating the relaxation, however, is a computationally demanding task, and only…
The Angular Constrained Minimum Spanning Tree Problem ($\alpha$-MSTP) is defined in terms of a complete undirected graph $G=(V,E)$ and an angle $\alpha \in (0,2\pi]$. Vertices of $G$ define points in the Euclidean plane while edges, the…
The goal of this paper is to get truly subcubic algorithms for Min-Plus product for less structured inputs than what was previously known, and to apply them to versions of All-Pairs Shortest Paths (APSP) and other problems. The results are…
Semidefinite programming (SDP) is a central topic in mathematical optimization with extensive studies on its efficient solvers. In this paper, we present a proof-of-principle sublinear-time algorithm for solving SDPs with low-rank…
We study two fundamental problems in computational geometry: finding the maximum inscribed ball (MaxIB) inside a bounded polyhedron defined by $m$ hyperplanes, and the minimum enclosing ball (MinEB) of a set of $n$ points, both in…
We consider the convergence behavior using the relaxed Peaceman-Rachford splitting method to solve the monotone inclusion problem $0 \in (A + B)(u)$, where $A, B: \Re^n \rightrightarrows \Re^n$ are maximal $\beta$-strongly monotone…
An accelerated block coordinate descent (ABCD) method in Hilbert space is analyzed to solve the sparse optimal control problem via its dual. The finite element approximation of this method is investigated and convergence results are…
We propose a new integer programming formulation for the problem of finding a maximum stable set of a graph based on representatives of stable sets. In addition, we investigate exact solutions provided by a Lagrangian decomposition of this…
Recent advances in symbolic dynamic programming (SDP) combined with the extended algebraic decision diagram (XADD) data structure have provided exact solutions for mixed discrete and continuous (hybrid) MDPs with piecewise linear dynamics…
In this work, we study the problem of finding approximate, with minimum support set, solutions to matrix max-plus equations, which we call sparse approximate solutions. We show how one can obtain such solutions efficiently and in polynomial…
Understanding and approximating extremal energy states of local Hamiltonians is a central problem in quantum physics and complexity theory. Recent work has focused on developing approximation algorithms for local Hamiltonians, and in…