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Gradient clipping is commonly used in training deep neural networks partly due to its practicability in relieving the exploding gradient problem. Recently, \citet{zhang2019gradient} show that clipped (stochastic) Gradient Descent (GD)…
Learning-based methods have gained attention as general-purpose solvers due to their ability to automatically learn problem-specific heuristics, reducing the need for manually crafted heuristics. However, these methods often face…
In the bounded-degree cut problem, we are given a multigraph $G=(V,E)$, two disjoint vertex subsets $A,B\subseteq V$, two functions $\mathrm{u}_A, \mathrm{u}_B:V\to \{0,1,\ldots,|E|\}$ on $V$, and an integer $k\geq 0$. The task is to…
In this work we propose an accelerated stochastic learning system for very large-scale applications. Acceleration is achieved by mapping the training algorithm onto massively parallel processors: we demonstrate a parallel, asynchronous GPU…
Matching and partitioning problems are fundamentals of computer vision applications with examples in multilabel segmentation, stereo estimation and optical-flow computation. These tasks can be posed as non-convex energy minimization…
This paper studies binary quadratic programs in which the objective is defined by a Euclidean distance matrix, subject to a general polyhedral constraint set. This class of nonconcave maximisation problems includes the capacitated,…
Scalable addressing of high dimensional constrained combinatorial optimization problems is a challenge that arises in several science and engineering disciplines. Recent work introduced novel application of graph neural networks for solving…
Bilevel optimization has been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel optimization problem, where the lower-level optimization problem is convex with…
Goemans and Williamson designed a 0.878-approximation algorithm for Max-Cut in undirected graphs [JACM'95]. Khot, Kindler, Mosel, and O'Donnel showed that the approximation ratio of the Goemans-Williamson algorithm is optimal assuming…
Large-scale linear programs (LPs) arise in many decision systems, including ranking, allocation, and matching problems that must be solved repeatedly at massive scale. Prior work such as ECLIPSE and LinkedIn's open-source DuaLip showed that…
We approach the Max-3-Cut problem through the lens of maximizing complex-valued quadratic forms and demonstrate that low-rank structure in the objective matrix can be exploited, leading to alternative algorithms to classical semidefinite…
We propose a novel approach to compute the MAXCUT in attributed graphs, i.e., graphs with features associated with nodes and edges. Our approach works well on any kind of graph topology and can find solutions that jointly optimize the…
We introduce a distributed adaptive quadrature method that formulates multidimensional integration as a hierarchical domain decomposition problem on multi-GPU architectures. The integration domain is recursively partitioned into subdomains…
In this paper, we address the challenge of solving large-scale graph-structured nonlinear programs (gsNLPs) in a scalable manner. GsNLPs are problems in which the objective and constraint functions are associated with nodes on a graph and…
We consider the graph $k$-partitioning problem under the min-max objective, termed as Minmax $k$-cut. The input here is a graph $G=(V,E)$ with non-negative edge weights $w:E\rightarrow \mathbb{R}_+$ and an integer $k\geq 2$ and the goal is…
Neuroscientists fit morphologically and biophysically detailed neuron simulations to physiological data, often using evolutionary algorithms. However, such gradient-free approaches are computationally expensive, making convergence slow when…
This paper presents a novel stochastic gradient descent algorithm for constrained optimization. The proposed algorithm randomly samples constraints and components of the finite sum objective function and relies on a relaxed logarithmic…
Quantum algorithms are getting extremely popular due to their potential to significantly outperform classical algorithms. Yet, applying quantum algorithms to optimization problems meets challenges related to the efficiency of quantum…
Graph Neural Networks (GNNs) have shown impressive performance in graph representation learning, but they face challenges in capturing long-range dependencies due to their limited expressive power. To address this, Graph Transformers (GTs)…
We consider differential Lyapunov and Riccati equations, and generalized versions thereof. Such equations arise in many different areas and are especially important within the field of optimal control. In order to approximate their…