A unifying modeling abstraction for infinite-dimensional optimization

Pulsipher, Joshua L.; Zhang, Weiqi; Hongisto, Tyler J.; Zavala, Ví­ctor M.

doi:10.1016/j.compchemeng.2021.107567

Cited by 15 publications

(4 citation statements)

References 45 publications

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“…446 Figure 3 depicts a numerically solution 447 using Julia and the InfiniteOpt.jl package 448 [36] for the optimal control along with the 449 resulting trajectories for the state variables 450 for the first 200 days. The weight and max-451 imum control are w = 0.01, and u max = 0.8, 452 respectively.…”

Section: Optimal Controlmentioning

confidence: 99%

Vaccination and collective action under social norms

Morsky

2024

Preprint

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Social dynamics are an integral part of the spread of disease affecting contact rates as well as the adoption of pharmaceutical and non-pharmaceutical interventions. When vaccines provide waning immunity, efficient and timely uptake of boosters is required to maintain protection and flatten the curve of infections. How then do social dynamics affect the timely uptake of vaccines and thereby the course of an epidemic? To explore this scenario, a behavioural-epidemiological is developed here. It features a tipping-point dynamic for the uptake of vaccines that combines the risk of infection, perceived morbidity risk of the vaccine, and social payoffs for deviating from the vaccination decision making of others. The social payoffs are derived from a social norm of conformity, and they create a collective action problem. A key finding driven by this dilemma is that waves of vaccine uptake and infections can occur due to inefficient and delayed uptake of boosters. This results in a nonlinear response of the infection load to the transmission rate: an intermediate transmission rate can result in greater prevalence of disease relative to more or less transmissible diseases. Further, global information about the prevalence of the disease and vaccine uptake increases the infection load and peak relative to information restricted to individuals' contact networks. Thus, decisions driven by local information can mitigate the collective action problem across the population. Finally, the optimal public policy program to promote boosters is shown to be one that focuses on overcoming the social inertia to vaccinate at the start of an epidemic.

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Section: Optimal Controlmentioning

confidence: 99%

Vaccination and collective action under social norms

Morsky

2024

Preprint

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“… 2019 ) Direct, Indirect Python, C++, Julia PSOPT (Becerra 2010 ) Direct Python, C++ InfiniteOpt.jl (Pulsipher et al. 2022 ) Direct Julia DifferentialEquations.jl (Rackauckas and Nie 2017 ) Indirect Julia TrajectoryOptimization.jl (Howell et al. 2019 ) DP Julia …”

Section: Comparison and Combination With Traditional Optimal Control ...mentioning

confidence: 99%

Optimal control by deep learning techniques and its applications on epidemic models

Yin

Song

2023

J. Math. Biol.

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We represent the optimal control functions by neural networks and solve optimal control problems by deep learning techniques. Adjoint sensitivity analysis is applied to train the neural networks embedded in differential equations. This method can not only be applied in classic epidemic control problems, but also in epidemic forecasting, discovering unknown mechanisms, and the ideas behind can give new insights to traditional mathematical epidemiological problems.

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“…DifferentialEquations.jl (Rackauckas & Nie, 2017) is a suite for numerically solving differential equations written in Julia, which includes features for parameter estimation and Bayesian analysis. InfiniteOpt.jl (Pulsipher et al, 2022) provides a general mathematical abstraction to express and solve infinite-dimensional optimization problems including with PDEs in the constraints handled by finitedifferences. TopOpt.jl (Huang & Tarek, 2021) is a package for topology optimization.…”

Section: Statement Of Needmentioning

confidence: 99%

PDENLPModels.jl: An NLPModel API for Optimization Problems with PDE-Constraints

Migot¹,

Orban²,

Siqueira³

2022

JOSS

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Shape optimization, optimal control, and parameter estimation of systems governed by partial differential equations (PDE) give rise to a class of problems known as PDE-constrained optimization (Hinze et al., 2008). PDENLPModels.jl is a Julia (Bezanson et al., 2017) package for modeling and discretizing optimization problems with mixed algebraic and PDE in the constraints. The general form of the problems over some domain Ω ⊂ ℝ 𝑑 is minimizewhere 𝑦 ∶ Ω → 𝒴 is the state, 𝑢 ∶ Ω → 𝒰 is the control, and 𝜃 ∈ ℝ 𝑘 are algebraic variables. 𝐽 ∶ 𝒴 × 𝒰 × ℝ 𝑘 → ℝ and 𝑒 ∶ 𝒴 × 𝒰 × ℝ 𝑘 → 𝒞 are smooth mappings. (𝒴, ‖ ⋅ ‖ 𝒴 ), (𝒰, ‖ ⋅ ‖ 𝒰 ), and (𝒞, ‖ ⋅ ‖ 𝒞 ) are real Banach spaces, 𝑙 𝜃 , 𝑢 𝜃 ∈ ℝ 𝑘 are bounds on 𝜃, and 𝑙 𝑦𝑢 , 𝑢 𝑦𝑢 ∶ Ω → 𝒴 × 𝒰 are functional bounds on the controls and states.After discretization of the domain Ω, the integral, and the derivatives, the resulting problem is a nonlinear optimization problem of the form minimize 𝑥∈ℝ 𝑁 𝑦 +𝑁 𝑢 +𝑁 𝜃 𝑓(𝑥) subject to 𝑐(𝑥) = 0, 𝑙 ≤ 𝑥 ≤ 𝑢,

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A unifying modeling abstraction for infinite-dimensional optimization

Cited by 15 publications

References 45 publications

Vaccination and collective action under social norms

Vaccination and collective action under social norms

Optimal control by deep learning techniques and its applications on epidemic models

PDENLPModels.jl: An NLPModel API for Optimization Problems with PDE-Constraints

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