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Quantum computing holds great potential to accelerate the process of solving complex combinatorial optimization problems. The Distributed Quantum Approximate Optimization Algorithm (DQAOA) addresses high-dimensional, dense problems using…
Combinatorial optimization problems on graphs have broad applications in science and engineering. The Quantum Approximate Optimization Algorithm (QAOA) is a method to solve these problems on a quantum computer by applying multiple rounds of…
Factor graph optimization serves as a fundamental framework for robotic perception, enabling applications such as pose estimation, simultaneous localization and mapping (SLAM), structure-from-motion (SfM), and situational awareness.…
Developing a contemporary optimal transport (OT) solver requires navigating trade-offs among several critical requirements: GPU parallelization, scalability to high-dimensional problems, theoretical convergence guarantees, empirical…
In a recent paper, Parikh and Boyd describe a method for solving a convex optimization problem, where each iteration involves evaluating a proximal operator and projection onto a subspace. In this paper we address the critical practical…
We explore how the big-three computing paradigms -- symmetric multi-processor (SMC), graphical processing units (GPUs), and cluster computing -- can together be brought to bare on large-data Gaussian processes (GP) regression problems via a…
TMAC is a toolbox written in C++11 that implements algorithms based on a set of modern methods for large-scale optimization. It covers a variety of optimization problems, which can be both smooth and nonsmooth, convex and nonconvex, as well…
We design, implement, and evaluate GPU-based algorithms for the maximum cardinality matching problem in bipartite graphs. Such algorithms have a variety of applications in computer science, scientific computing, bioinformatics, and other…
The periodic Gaussian process (PGP) has been increasingly used to model periodic data due to its high accuracy. Yet, computing the likelihood of PGP has a high computational complexity of $\mathcal{O}\left(n^{3}\right)$ ($n$ is the data…
In this paper we discuss Grover Adaptive Search (GAS) for Constrained Polynomial Binary Optimization (CPBO) problems, and in particular, Quadratic Unconstrained Binary Optimization (QUBO) problems, as a special case. GAS can provide a…
In this paper we study the generalized vertex cover problem (GVC), which is a generalization of various well studied combinatorial optimization problems. GVC is shown to be equivalent to the unconstrained binary quadratic programming…
Principal component analysis (PCA) is a key statistical technique for multivariate data analysis. For large data sets the common approach to PCA computation is based on the standard NIPALS-PCA algorithm, which unfortunately suffers from…
Machine learning models made up of millions or billions of parameters are trained and served on large multi-GPU systems. As models grow in size and execute on more GPUs, the collective communications used in these applications become a…
For Hermitian positive definite linear systems and eigenvalue problems, the eigCG algorithm is a memory efficient algorithm that solves the linear system and simultaneously computes some of its eigenvalues. The algorithm is based on the…
Genetic Programming (GP) is a computationally intensive technique which also has a high degree of natural parallelism. Parallel computing architectures have become commonplace especially with regards Graphics Processing Units (GPU). Hence,…
Gaussian processes (GPs) provide a powerful framework for extrapolation, interpolation, and noise removal in regression and classification. This paper considers constraining GPs to arbitrarily-shaped domains with boundary conditions. We…
Generalised planning (GP) refers to the task of synthesising programs that solve families of related planning problems. We introduce a novel, yet simple method for GP: given a set of training problems, for each problem, compute an optimal…
This work addresses integrating probabilistic propositional logic constraints into the distribution encoded by a probabilistic circuit (PC). PCs are a class of tractable models that allow efficient computations (such as conditional and…
High-dimensional optimization is a critical challenge for operating large-scale scientific facilities. We apply a physics-informed Gaussian process (GP) optimizer to tune a complex system by conducting efficient global search. Typical GP…
In recent years, progress in adaptive graph signal processing algorithms has provided effective solutions for processing signals defined on graph structures. As a classical strategy in information theory, the Generalized Maximum Correntropy…