Nonlinear programming strategies on high-performance computers

Kang, Jia; Chiang, Nai-Yuan; Laird, Carl D.; Zavala, Ví­ctor M.

doi:10.1109/cdc.2015.7402938

Cited by 20 publications

(17 citation statements)

References 35 publications

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“…The permutation does not affect the eigenvalues of the matrix. The BBD system (14) can be solved in parallel by using a Schur complement decomposition approach [45,50]. This requires the solution of the linear algebra systems:…”

Section: Structured Linear Algebramentioning

confidence: 99%

Scalable Nonlinear Programming Framework for Parameter Estimation in Dynamic Biological System Models

Shin

Venturelli

Zavala

2018

Preprint

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We present a nonlinear programming (NLP) framework for the scalable solution of parameter estimation problems that arise in dynamic modeling of biological systems. Such problems are computationally challenging because they often involve highly nonlinear and stiff differential equations as well as many experimental data sets and parameters. The proposed framework uses cutting-edge modeling and solution tools which are computationally efficient, robust, and easy-to-use. Specifically, our framework uses a time discretization approach that: i) avoids repetitive simulations of the dynamic model, ii) enables fully algebraic model implementations and computation of derivatives, and iii) enables the use of computationally efficient nonlinear interior point solvers that exploit sparse and structured linear algebra techniques. We demonstrate these capabilities by solving estimation problems for synthetic human gut microbiome community models. We show that an instance with 156 parameters, 144 differential equations, and 1,704 experimental data points can be solved in less than 3 minutes using our proposed framework (while an off-the-shelf simulation-based solution framework requires over 7 hours). We also create large instances to show that the proposed framework is scalable and can solve problems with up to 2,352 parameters, 2,304 differential equations, and 20,352 data points in less than 15 minutes. Competing methods reported in the computational biology literature cannot address problems of this level of complexity. The proposed framework is flexible, can be broadly applied to dynamic models of biological systems, and enables the implementation of sophisticated estimation techniques to quantify parameter uncertainty, to diagnose observability/uniqueness issues, to perform model selection, and to handle outliers. Author summaryConstructing and validating dynamic models of biological systems spanning biomolecular networks to ecological systems is a challenging problem. Here we present a scalable computational framework to rapidly infer parameters in complex dynamic models of biological systems from large-scale experimental data. The framework was applied to infer parameters of a synthetic microbial community model from large-scale time series data. We also demonstrate that this framework can be used to analyze parameter uncertainty, to diagnose whether the experimental data are sufficient to PLOS 1/28 uniquely determine the parameters, to determine the model that best describes the data, and to infer parameters in the face of data outliers. PLOS

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Section: Structured Linear Algebramentioning

confidence: 99%

Scalable Nonlinear Programming Framework for Parameter Estimation in Dynamic Biological System Models

Shin

Venturelli

Zavala

2018

Preprint

Self Cite

View full text Add to dashboard Cite

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“…We thus have that the linear system is block-bordered diagonal and thus can be solved using a Schur complement decomposition approach [27,29]. The Schur complement is of the same size as the dimension of w 0 and λ and is often a dense matrix.…”

Section: Problem Decompositionmentioning

confidence: 99%

“…The Schur complement is of the same size as the dimension of w 0 and λ and is often a dense matrix. This approach exhibits linear scaling in the number of scenarios if the number of coupling variables and constraints is of a few thousand variables and constraints [49,27]. In particular, the dense factorization of large Schur complement matrices dominates scaling in the scenario space.…”

Section: Problem Decompositionmentioning

confidence: 99%

Scalable modeling and solution of stochastic multiobjective optimization problems

Cao

Fuentes-Cortés

Chen

et al. 2017

Computers & Chemical Engineering

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We present a scalable computing framework for the solution stochastic multiobjective optimization problems. The proposed framework uses a nested conditional value-at-risk (nCVaR) objective to find compromise solutions among conflicting random objectives. We prove that the associated nCVaR minimization problem can be cast as a standard stochastic programming problem with expected value (linking) constraints. We also show that these problems can be implemented in a modular and compact manner using PLASMO (a Julia-based structured modeling framework) and can be solved efficiently using PIPS-NLP (a parallel nonlinear solver). We apply the framework to a CHP design study in which we seek to find compromise solutions that trade-off cost, water, and emissions in the face of uncertainty in electricity and water demands.

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“…This structure can be exploited with efficient implementations of direct [7] or iterative [8] sparse linear algebra algorithms [5], [6], [9].…”

Section: A Dynamic Optimizationmentioning

confidence: 99%

Computer architectures to close the loop in real-time optimization

Kerrigan

Constantinides

Suardi

et al. 2015

2015 54th IEEE Conference on Decision and Control (CDC)

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Abstract-Many modern control, automation, signal processing and machine learning applications rely on solving a sequence of optimization problems, which are updated with measurements of a real system that evolves in time. The solutions of each of these optimization problems are then used to make decisions, which may be followed by changing some parameters of the physical system, thereby resulting in a feedback loop between the computing and the physical system. Real-time optimization is not the same as 'fast' optimization, due to the fact that the computation is affected by an uncertain system that evolves in time. The suitability of a design should therefore not be judged from the optimality of a single optimization problem, but based on the evolution of the entire cyber-physical system. The algorithms and hardware used for solving a single optimization problem in the office might therefore be far from ideal when solving a sequence of real-time optimization problems. Instead of there being a single, optimal design, one has to trade-off a number of objectives, including performance, robustness, energy usage, size and cost. We therefore provide here a tutorial introduction to some of the questions and implementation issues that arise in real-time optimization applications. We will concentrate on some of the decisions that have to be made when designing the computing architecture and algorithm and argue that the choice of one informs the other.

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Nonlinear programming strategies on high-performance computers

Cited by 20 publications

References 35 publications

Scalable Nonlinear Programming Framework for Parameter Estimation in Dynamic Biological System Models

Scalable Nonlinear Programming Framework for Parameter Estimation in Dynamic Biological System Models

Scalable modeling and solution of stochastic multiobjective optimization problems

Computer architectures to close the loop in real-time optimization

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