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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Running Primal-Dual Gradient Method for Time-Varying Nonconvex Problems

This paper focuses on a time-varying constrained nonconvex optimization problem, and considers the synthesis and analysis of online regularized primal-dual gradient methods to track a Karush-Kuhn-Tucker (KKT) trajectory. The proposed regularized primal-dual gradient method is implemented in a running fashion, in the sense that the underlying optimization problem changes during the execution of the algorithms. In order to study its performance, we first derive its continuous-time limit as a system of differential inclusions. We then study sufficient conditions for tracking a KKT trajectory, and also derive asymptotic bounds for the tracking error (as a function of the time-variability of a KKT trajectory). Further, we provide a set of sufficient conditions for the KKT trajectories not to bifurcate or merge, and also investigate the optimal choice of the parameters of the algorithm. Illustrative numerical results for a time-varying nonconvex problem are provided.

differential inclusion↗
DOE OSTI2022

A nonsmooth nonconvex optimization algorithm for two-stage optimization problems

An optimization algorithm for a group of nonsmooth nonconvex problems inspired by two-stage stochastic programming problems is proposed. The main challenges for these problems include (1) the problems lack the popular lower-type properties such as prox-regularity assumed in many nonsmooth nonconvex optimization algorithms, (2) the objective can not be analytically expressed and (3) the evaluation of function values and subgradients are computationally expensive. To address these challenges, this report first examines the properties that exist in many two-stage problems, specifically upper-C 2 objectives. Then, we show that quadratic penalty method for securityconstrained alternating current optimal power flow (SCACOPF) contingency problems can make the contingency solution functions upper-C 2 . Based on these observations, a simplified bundle algorithm that bears similarity to sequential quadratic programming (SQP) method is proposed. It is more efficient in implementation and computation compared to conventional bundle methods. Global convergence analysis of the algorithm is presented under novel and reasonable assumptions. The proposed algorithm therefore fills the gap of theoretical convergence for smoothed SCACOPF problems. The inconsistency that might arise in our treatment of the constraints are addressed through a penalty algorithm whose convergence analysis is also provided. Finally, theoretical capabilities and numerical performance of the algorithm are demonstrated through numerical examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Multistart algorithm for identifying all optima of nonconvex stochastic functions

Here, we propose a multistart algorithm to identify all local minima of a constrained, nonconvex stochastic optimization problem. The algorithm uniformly samples points in the domain and then starts a local stochastic optimization run from any point that is the "probabilistically best" point in its neighborhood. Under certain conditions, our algorithm is shown to asymptotically identify all local optima with high probability; this holds even though our algorithm is shown to almost surely start only finitely many local stochastic optimization runs. We demonstrate the performance of an implementation of our algorithm on nonconvex stochastic optimization problems, including identifying optimal variational parameters for the quantum approximate optimization algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Nonconvex regularization for sparse neural networks

Convex ℓ 1 regularization using an infinite dictionary of neurons has been suggested for constructing neural networks with desired approximation guarantees, but can be affected by an arbitrary amount of over-parametrization. This can lead to a loss of sparsity and result in networks with too many active neurons for the given data, in particular if the number of data samples is large. As a remedy, in this paper, a nonconvex regularization method is investigated in the context of shallow ReLU networks: We prove that in contrast to the convex approach, any resulting (locally optimal) network is finite even in the presence of infinite data (i.e., if the data distribution is known and the limiting case of infinite samples is considered). Moreover, here we show that approximation guarantees and existing bounds on the network size for finite data are maintained.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Randomized Federated Learning Methods for Nonsmooth, Nonconvex, and Hierarchical Optimization (Final Technical Report)

This final technical report summarizes the outcomes of a DOE-funded project on federated scientific machine learning (FL) under nonsmooth, nonconvex, and hierarchical optimization settings. The project develops new mathematical models, algorithms, and theoretical guarantees for decentralized stochastic, bilevel, and minimax optimization problems arising in DOE mission-relevant applications. A unified framework of randomized and zeroth-order federated optimization methods is introduced, providing provable convergence, communication efficiency, and sample-complexity guarantees. The report documents algorithmic design, theoretical analysis, and empirical validation of the proposed federated learning methods. The project also contributes to workforce development through graduate training and dissemination of results via publications and seminars.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Manifold Sampling for Optimizing Nonsmooth Nonconvex Compositions

Here we propose a manifold sampling algorithm for minimizing a nonsmooth composition $f= h\circ F$, where we assume $h$ is nonsmooth and may be inexpensively computed in closed form and $F$ is smooth but its Jacobian may not be available. We additionally assume that the composition $h\circ F$ defines a continuous selection. Manifold sampling algorithms can be classified as model-based derivative-free methods, in that models of $F$ are combined with particularly sampled information about $h$ to yield local models for use within a trust-region framework. We demonstrate that cluster points of the sequence of iterates generated by the manifold sampling algorithm are Clarke stationary. We consider the tractability of three particular subproblems generated by the manifold sampling algorithm and the extent to which inexact solutions to these subproblems may be tolerated. Numerical results demonstrate that manifold sampling as a derivative-free algorithm is competitive with state-of-the-art algorithms for nonsmooth optimization that utilize first-order information about $f$.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Recent Advances of PyROS: A Pyomo Solver for Nonconvex Two-Stage Robust Optimization in Process Systems Engineering

This poster highlights uncertainty and technical risk reduction capabilities in CCSI2, with a focus on robust optimization. It presents recent advances of the two-stage robust optimization (RO) solver PyROS and applications to advanced energy systems optimization. To demonstrate the computational performance and reliability of PyROS, a benchmarking study on a library of over 8,500 small-scale RO problems is presented. Further, PyROS is used to obtain robust system designs of a MEA-based CO2 absorber under uncertainty in the thermodynamic property models for a variety of CO2 capture rate threshold requirements. Overall, the results demonstrate that the PyROS solver, including recent extensions to multi-stage RO settings, provides a reliable avenue to optimize the design and operation of advanced energy systems subject to various sources of parametric uncertainty.

Sherman, Jason↗
DOE OSTI2024

Recent Advances of PyROS: A Pyomo Solver for Nonconvex Two-Stage Robust Optimization in Process Systems Engineering

This poster highlights uncertainty and technical risk reduction capabilities in CCSI2, with a focus on robust optimization. It presents recent advances of the two-stage robust optimization (RO) solver PyROS and applications to advanced energy systems optimization. To demonstrate the computational performance and reliability of PyROS, a benchmarking study on a library of over 8,500 small-scale RO problems is presented. Further, PyROS is used to obtain robust system designs of a MEA-based CO2 absorber under uncertainty in the thermodynamic property models for a variety of CO2 capture rate threshold requirements. Overall, the results demonstrate that the PyROS solver, including recent extensions to multi-stage RO settings, provides a reliable avenue to optimize the design and operation of advanced energy systems subject to various sources of parametric uncertainty.

Sherman, Jason↗
DOE OSTI2024

Nonconvex Robust Optimization for the Design and Operation of Advanced Energy Systems Using PyROS

This work discusses recent advances of the two-stage robust optimization (RO) solver PyROS and applications to advanced energy systems optimization. To demonstrate the computational performance and reliability of PyROS, a study on a monoethanolamine (MEA)-based CO2 absorption flowsheet is presented. (Near-)robust feasible designs for CO2 absorption flowsheet at high carbon capture are obtained with the PyROS solver. The results demonstrate that the PyROS solver, including recent extensions to multi-stage RO settings, provides a reliable avenue to optimize the design and operation of advanced energy systems subject to various sources of parametric uncertainty.

Sherman, Jason↗
DOE OSTI2024

Recent Advances of PyROS: A Pyomo Solver for Nonconvex Two-Stage Robust Optimization in Process Systems Engineering

The document presents recent algorithmic and implementation advances of the two-stage robust optimization (RO) solver PyROS, and a benchmarking study which demonstrates the utility of PyROS for two-stage RO problems. The advances include extensions of the scope of PyROS to models with uncertain variable bounds, improvements to the initializations of the subproblems used by the underlying cutting set algorithm, and extensions of the uncertainty set interfaces. The benchmarking study is performed on a library of over 8,500 instances, with variations in the nonlinearities, degree-of-freedom partitioning, uncertainty sets, and polynomial decision rule approximations. An amine-based CO2 capture case study is presented to demonstrate the utility of PyROS for large-scale process models. Overall, the results highlight the effectiveness of PyROS for obtaining robust solutions to optimization problems with uncertain equality constraints.

Sherman, Jason↗
DOE OSTI2023

Recent Advances in PyROS: The Pyomo Solver for Two-Stage Nonconvex Robust Optimization

The slides present recent algorithmic and implementation advances of the two-stage robust optimization (RO) solver PyROS, and a benchmarking study which demonstrates the utility of PyROS for two-stage RO problems. The advances include extensions of the scope of PyROS to models with uncertain variable bounds, improvements to the initializations of the subproblems used by the underlying cutting set algorithm, and extensions of the uncertainty set interfaces. The benchmarking study is performed on a library of over 8,500 instances, with variations in the nonlinearities, degree-of-freedom partitioning, uncertainty sets, and polynomial decision rule approximations. Overall, the results highlight the effectiveness of PyROS for obtaining robust solutions to optimization problems with uncertain equality constraints.

Sherman, Jason↗
DOE OSTI2023

Nonconvex Two-Stage Robust Optimization of an Amine-Based CO2 Capture System

These summary slides highlight uncertainty and technical risk reduction capabilities in CCSI2, with a focus on robust optimization. PyROS is used to obtain robust system designs of a MEA-based CO2 absorber under uncertainty in the thermodynamic property models for a variety of CO2 capture rate threshold requirements.

Sherman, Jason↗