Related papers: A Graph-Based, Distributed Memory, Modeling Abstra…
We present a general graph-based modeling abstraction for optimization that we call an OptiGraph. Under this abstraction, any optimization problem is treated as a hierarchical hypergraph in which nodes represent optimization subproblems and…
We present a graph-theoretic modeling approach for hierarchical optimization that leverages the OptiGraph abstraction implemented in the Julia package Plasmo.jl. We show that the abstraction is flexible and can effectively capture complex…
We present graph-based modeling abstractions to represent cyber-physical dependencies arising in complex systems. Specifically, we propose an algebraic graph abstraction to capture physical connectivity in complex optimization models and a…
Benders decomposition is a widely used method for solving large optimization problems, but its performance is often hindered by the repeated solution of subproblems. We propose a flexible and modular algorithmic framework for accelerating…
Hierarchical optimization architectures are used in power systems to manage disturbances and phenomena that arise at multiple spatial and temporal scales. We present a graph modeling abstraction for representing such architectures and an…
Nonlinear optimization problems are found at the heart of real-time operations of critical infrastructures. These problems are computationally challenging because they embed complex physical models that exhibit space-time dynamics. We…
Graph theory provides a convenient framework for modeling and solving structured optimization problems. Under this framework, the modeler can arrange/assemble the components of an optimization model (variables, constraints, objective…
Distributed memory machines equipped with CPUs and GPUs (hybrid computing nodes) are hard to program because of the multiple layers of memory and heterogeneous computing configurations. In this paper, we introduce a region template…
We propose a multi-scale approach for computing abstractions of dynamical systems, that incorporates both local and global optimal control to construct a goal-specific abstraction. For a local optimal control problem, we not only design the…
Distributed abstract programs are a novel class of distributed optimization problems where (i) the number of variables is much smaller than the number of constraints and (ii) each constraint is associated to a network node. Abstract…
Machine Learning (ML) techniques are indispensable in a wide range of fields. Unfortunately, the exponential increase of dataset sizes are rapidly extending the runtime of sequential algorithms and threatening to slow future progress in ML.…
Graph databases have been the subject of significant research and development. Problems such as modularity, centrality, alignment, and clustering have been formalized and solved in various application contexts. In this paper, we focus on…
While high-level data parallel frameworks, like MapReduce, simplify the design and implementation of large-scale data processing systems, they do not naturally or efficiently support many important data mining and machine learning…
The paper addresses large-scale, convex optimization problems that need to be solved in a distributed way by agents communicating according to a random time-varying graph. Specifically, the goal of the network is to minimize the sum of…
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…
This paper presents a novel meta algorithm, Partition-Merge (PM), which takes existing centralized algorithms for graph computation and makes them distributed and faster. In a nutshell, PM divides the graph into small subgraphs using our…
Datasets encountered in scientific and engineering applications appear in complex formats (e.g., images, multivariate time series, molecules, video, text strings, networks). Graph theory provides a unifying framework to model such datasets…
This paper proposes distributed algorithms to solve robust convex optimization (RCO) when the constraints are affected by nonlinear uncertainty. We adopt a scenario approach by randomly sampling the uncertainty set. To facilitate the…
Infinite-dimensional optimization (InfiniteOpt) problems involve modeling components (variables, objectives, and constraints) that are functions defined over infinite-dimensional domains. Examples include continuous-time dynamic…
Efficient processing of large-scale graphs in distributed environments has been an increasingly popular topic of research in recent years. Inter-connected data that can be modeled as graphs arise in application domains such as machine…