arXiv subjects

Oscar Dowson

Publications and source records attributed to Oscar Dowson.

9 recordsLinked to original sources

arXiv2025

Nonlinear Optimization with GPU-Accelerated Neural Network Constraints

We propose a reduced-space formulation for optimizing over trained neural networks where the network's outputs and derivatives are evaluated on a GPU. To do this, we treat the neural network as a "gray box" where intermediate variables and constraints are not exposed to the optimization solver. Compared to the full-space formulation, in which intermediate variables and constraints are exposed to the optimization solver, the reduced-space formulation leads to faster solves and fewer iterations in an interior point method. We demonstrate the benefits of this method on two optimization problems: Adversarial generation for a classifier trained on MNIST images and security-constrained optimal power flow with transient feasibility enforced using a neural network surrogate.

cs.LG↗

arXiv2025

MDP modeling for multi-stage stochastic programs

We study a class of multi-stage stochastic programs, which incorporate modeling features from Markov decision processes (MDPs). This class includes structured MDPs with continuous action and state spaces. We extend policy graphs to include decision-dependent uncertainty for one-step transition probabilities as well as a limited form of statistical learning. We focus on the expressiveness of our modeling approach, illustrating ideas with a series of examples of increasing complexity. As a solution method, we develop new variants of stochastic dual dynamic programming, including approximations to handle non-convexities.

cs.LG↗

arXiv2025

MultiObjectiveAlgorithms.jl: a Julia package for solving multi-objective optimization problems

We present MultiObjectiveAlgorithms.jl, an open-source Julia library for solving multi-objective optimization problems written in JuMP. MultiObjectiveAlgorithms.jl implements a number of different solution algorithms, which all rely on an iterative scalarization of the problem from a multi-objective optimization problem to a sequence of single-objective subproblems. As part of this work, we extended JuMP to support vector-valued objective functions. Because it is based on JuMP, MultiObjectiveAlgorithms.jl can use a wide variety of commercial and open-source solvers to solve the single-objective subproblems, and it supports problem classes ranging from linear, to conic, semi-definite, and general nonlinear. MultiObjectiveAlgorithms.jl is available at https://github.com/jump-dev/MultiObjectiveAlgorithms.jl under a MPL-2 license.

math.OC↗

arXiv2025

MathOptAI.jl: Embed trained machine learning predictors into JuMP models

We present \texttt{MathOptAI.jl}, an open-source Julia library for embedding trained machine learning predictors into a JuMP model. \texttt{MathOptAI.jl} can embed a wide variety of neural networks, decision trees, and Gaussian Processes into a larger mathematical optimization model. In addition to interfacing a range of Julia-based machine learning libraries such as \texttt{Lux.jl} and \texttt{Flux.jl}, \texttt{MathOptAI.jl} uses Julia's Python interface to provide support for PyTorch models. When the PyTorch support is combined with \texttt{MathOptAI.jl}'s gray-box formulation, the function, Jacobian, and Hessian evaluations associated with the PyTorch model are offloaded to the GPU in Python, while the rest of the nonlinear oracles are evaluated on the CPU in Julia. \MathOptAI is available at https://github.com/lanl-ansi/MathOptAI.jl under a BSD-3 license.

cs.LG↗

arXiv2024

Formulations and scalability of neural network surrogates in nonlinear optimization problems

We compare full-space, reduced-space, and gray-box formulations for representing trained neural networks in nonlinear constrained optimization problems. We test these formulations on a transient stability-constrained, security-constrained alternating current optimal power flow (SCOPF) problem where the transient stability criteria are represented by a trained neural network surrogate. Optimization problems are implemented in JuMP and trained neural networks are embedded using a new Julia package: MathOptAI.jl. To study the bottlenecks of the three formulations, we use neural networks with up to 590 million trained parameters. The full-space formulation is bottlenecked by the linear solver used by the optimization algorithm, while the reduced-space formulation is bottlenecked by the algebraic modeling environment and derivative computations. The gray-box formulation is the most scalable and is capable of solving with the largest neural networks tested. It is bottlenecked by evaluation of the neural network's outputs and their derivatives, which may be accelerated with a graphics processing unit (GPU). Leveraging the gray-box formulation and GPU acceleration, we solve our test problem with our largest neural network surrogate in 2.5$\times$ the time required for a simpler SCOPF problem without the stability constraint.

cs.LG↗

arXiv2023

Capacity planning of renewable energy systems using stochastic dual dynamic programming

We present a capacity expansion model for deciding the new electricity generation and transmission capacity to complement an existing hydroelectric reservoir system. The objective is to meet a forecast demand at least expected cost, namely the capital cost of the investment plus the expected discounted operating cost of the system. The optimal operating policy for any level of capacity investment can be computed using stochastic dual dynamic programming. We show how to combine a multistage stochastic operational model of the hydro system with a capacity expansion model to create a single model that can be solved by existing open-source solvers for multistage stochastic programs without the need for customized decomposition algorithms. We illustrate our method by applying it to a model of the New Zealand electricity system and comparing the solutions obtained with those found in a previous study.

math.OC↗

arXiv2023

JuMP 1.0: Recent improvements to a modeling language for mathematical optimization

JuMP is an algebraic modeling language embedded in the Julia programming language. JuMP allows users to model optimization problems of a variety of kinds, including linear programming, integer programming, conic optimization, semidefinite programming, and nonlinear programming, and handles the low-level details of communicating with solvers. After nearly 10 years in development, JuMP 1.0 was released in March, 2022. In this short communication, we highlight the improvements to JuMP from recent releases up to and including 1.0.

cs.PL↗

arXiv2021

Assessing the Cost of Network Simplifications in Long-Term Hydrothermal Dispatch Planning Models

The sustainable utilization of hydro energy relies on accurate estimates of the opportunity cost of the water. This value is calculated through long-term hydrothermal dispatch problems (LTHDP), and the recent literature has raised awareness about the consequences of modeling simplifications in these problems. The inaccurate representation of Kirchhoff's voltage law under the premise of a DC power flow is an example. Under a non-linear AC model, however, the LTHDP becomes intractable, and the literature lacks an accurate evaluation method of different modeling alternatives. In this paper, we extend the state-of-the-art cost-assessment framework of network approximations for LTHDP and bring relevant and practical new insights. First, we increase the quality of the assessment by using an AC power flow to simulate and compare the performance of five policies based on different network approximations. Second, we find that the tightest network relaxation (based on semidefinite programming) is not the one exhibiting the best performance. Results show that the DC {power flow} with quadratic losses approximation exhibits the lowest expected cost and inconsistency gaps. Finally, its computational burden is lower than that exhibited by the semidefinite relaxation, whereas market distortions are significantly reduced in comparison to previously published benchmarks based on DC power flow.

math.OC↗

arXiv2020

MathOptInterface: a data structure for mathematical optimization problems

We introduce MathOptInterface, an abstract data structure for representing mathematical optimization problems based on combining pre-defined functions and sets. MathOptInterface is significantly more general than existing data structures in the literature, encompassing, for example, a spectrum of problems classes from integer programming with indicator constraints to bilinear semidefinite programming. We also outline an automated rewriting system between equivalent formulations of a constraint. MathOptInterface has been implemented in practice, forming the foundation of a recent rewrite of JuMP, an open-source algebraic modeling language in the Julia language. The regularity of the MathOptInterface representation leads naturally to a general file format for mathematical optimization we call MathOptFormat. In addition, the automated rewriting system provides modeling power to users while making it easy to connect new solvers to JuMP.

math.OC↗