SEARCH · Engineering Papers

Results for “Lagrangian dual”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

11 records

All sources NASA NTRS DOE OSTI

DOE OSTI2022

A Lagrangian dual method for two-stage robust optimization with binary uncertainties

This report presents a new exact method to calculate worst-case parameter realizations in two-stage robust optimization problems with categorical or binary-valued uncertain data. Traditional exact algorithms for these problems, notably Benders decomposition and column-and-constraint generation, compute worst-case parameter realizations by solving mixed-integer bilinear optimization subproblems. However, their numerical solution can be computationally expensive not only due to their resulting large size after reformulating the bilinear terms, but also because decision-independent bounds on their variables are typically unknown. We propose an alternative Lagrangian dual method that circumvents these difficulties and is readily integrated in either algorithm. We specialize the method to problems where the binary parameters switch on or off constraints as these are commonly encountered in applications, and discuss extensions to problems that lack relatively complete recourse and to those with integer recourse. Numerical experiments provide evidence of significant computational improvements over existing methods.

42 ENGINEERING↗

DOE OSTI2026

Dynamic Transmission Line Switching Amid Wildfire-Prone Weather Under Decision-Dependent Uncertainty

During dry and windy seasons, environmental conditions significantly increase the risk of wildfires, exposing power grids to disruptions caused by transmission line failures. Wildfire propagation exacerbates grid vulnerability, potentially leading to prolonged power outages. To address this challenge, we propose a multistage optimization model that dynamically adjusts transmission grid topology in response to wildfire propagation, aiming to develop an optimal response policy. By accounting for decision-dependent uncertainty, where line survival probabilities depend on usage, we employ distributionally robust optimization to model uncertainty in line survival distributions. We adapt the stochastic nested decomposition algorithm and derive a deterministic upper bound for its finite convergence. To enhance computational efficiency, we exploit the Lagrangian dual problem structure for a faster generation of Lagrangian cuts. Using realistic data from the California transmission grid, we demonstrate the superior performance of dynamic response policies against two-stage alternatives through a comprehensive case study. In addition, after solving the multistage formulation, we construct easy-to-implement policies that significantly reduce computational burden while maintaining good performance in real-time deployment. History: Accepted by Russell Bent, Area Editor for Network Optimization: Algorithms and Applications. Funding: This work was supported by the U.S. Department of Energy, Office of Electricity [Grant DE-AC02-05CH11231]. The work of R. Jiang was supported in part by the U.S. National Science Foundation, Division of Electrical, Communications and Cyber Systems [Grant ECCS-1845980] and the U.S. Air Force Office of Scientific Research [Grant FA9550-23-1-0323]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2025.1210 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2025.1210 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Estrada-Garcia, Juan-Alberto↗

DOE OSTI2022

A computationally efficient algorithm for computing convex hull prices

Electricity markets worldwide allow participants to bid non-convex production offers. While non-convex offers can more accurately reflect a resource's capabilities, they create challenges for market clearing processes. For example, system operators may be required to execute side payments to participants whose costs are not covered through energy sales as determined via traditional locational marginal pricing schemes. Convex hull pricing minimizes this and other types of side payments while providing uniform (i.e., locationally and temporally consistent) prices. Computing convex hull prices involves solving either a large-scale linear program or the Lagrangian dual of the corresponding non-convex scheduling problem. Further, the former approach requires explicit descriptions of market participants' convex hulls. While linear programs for computing convex hull prices are large, their structure is naturally decomposable by generators. Here, in this work, we propose and empirically analyze a Benders decomposition approach to computing convex hull prices that leverages recent advances in convex hull formulations for thermal generating units. We demonstrate across a large set of test instances that our decomposition approach only requires modest computational effort, obtaining solutions at least an order of magnitude faster than the equivalent large-scale linear programming approach. Overall, we provide a computationally feasible method for computing convex hull prices for industrial scale market clearing problems, enabling the possibility of practical adoption of this advanced pricing mechanism.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2021

Risk-averse optimization for resilience enhancement of complex engineering systems under uncertainties

With the growth of complexity and extent, large scale interconnected network systems, e.g., transportation networks or infrastructure networks, become more vulnerable to external disturbances. Hence, managing potential disruptive events during the design, operating, and recovery phase of an engineered system and therefore improving the system’s resilience is an important yet challenging task. Here, to ensure system resilience after the occurrence of failure events, this study proposes a mixed-integer linear programming (MILP) based restoration framework using heterogeneous dispatchable agents. The scenario-based stochastic optimization (SO) technique is adopted to deal with the inherent uncertainties imposed on the recovery process from nature. Moreover, different from conventional SO using deterministic equivalent formulations, the CVaR risk measure is implemented for this study because of the temporal sparsity of the decision making in applications such as the recovery from extreme events. The resulting restoration framework involves a large-scale MILP problem and thus an adequate decomposition technique i.e. modified Lagrangian dual decomposition, is also employed to achieve tractable computational complexity. Case study results based on the IEEE 37-bus test feeder demonstrate the benefits of using the proposed framework for resilience improvement as well as the advantages of adopting SO formulations.

42 ENGINEERING↗

DOE OSTI2021

A Computationally Efficient Algorithm for Computing Convex Hull Prices

Electricity markets worldwide allow participants to bid non-convex production offers. While non-convex offers can more accurately reflect a resource's capabilities, they create challenges for market clearing processes. For example, system operators may execute side payments when a participant’s cost is not covered through energy sale settlements from locational marginal pricing schemes, or when a participant incurs lost opportunity costs to follow the dispatch signal. Convex hull pricing minimizes these and other types of side payments while providing uniform (i.e., locationally and temporally consistent) prices. However, computing convex hull prices involves solving either a large-scale linear program - which in turn requires explicit descriptions of market participants’ convex hulls -or the Lagrangian dual of the corresponding non-convex scheduling problem. Here, we propose a computationally feasible and industrially scalable Benders decomposition approach to computing convex hull prices at least an order of magnitude faster than the current state-of-the-art while leveraging recent advances in convex hull formulations for thermal generating units.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2026

Extreme-scale EV charging infrastructure planning for last-mile delivery using high-performance parallel computing

Here, this paper addresses stochastic charger location and allocation problems under queue congestion for last-mile delivery using electric vehicles (EVs). The objective is to decide where to open charging stations and how many chargers of each type to install, subject to budgetary and waiting-time constraints. We formulate the problem as a mixed-integer non-linear program, where each station-charger pair is modeled as a multiserver queue with stochastic arrivals and service times to capture the notion of waiting in fleet operations. The model is extremely large, with billions of variables and constraints for a typical metropolitan area; even loading the model in solver memory is difficult, let alone solving it. To address this challenge, we develop a Lagrangian-based dual decomposition framework that decomposes the problem by station and leverages parallelization on high-performance computing systems, where the subproblems are solved by using a cutting plane method and their solutions are collected at the master level. We also develop a three-step rounding heuristic to transform the fractional subproblem solutions into feasible integral solutions. Computational experiments on data from the Chicago metropolitan area with hundreds of thousands of households and thousands of candidate stations show that our approach produces high-quality solutions in cases where existing exact methods cannot even load the model in memory. We also analyze various policy scenarios, demonstrating that combining existing depots with newly built stations under multiagency collaboration substantially reduces costs and congestion. These findings offer a scalable and efficient framework for developing sustainable large-scale EV charging networks.

Capacity allocation↗

DOE OSTI2023

Exploring non-invertible symmetries in free theories

Symmetries corresponding to local transformations of the fundamental fields that leave the action invariant give rise to (invertible) topological defects, which obey group-like fusion rules. One can construct more general (codimension-one) topological defects by specifying a map between gauge-invariant operators from one side of the defect and such operators on the other side. In this work, we apply such construction to Maxwell theory in four dimensions and to the free compact scalar theory in two dimensions. In the case of Maxwell theory, we show that a topological defect that mixes the field strength F and its Hodge dual *F can be at most an SO(2) rotation. For rational values of the bulk coupling and the θ-angle we find an explicit defect Lagrangian that realizes values of the SO(2) angle φ such that cos φ is also rational. We further determine the action of such defects on Wilson and ’t Hooft lines and show that they are in general non-invertible. We repeat the analysis for the free compact scalar Φ in two dimensions. In this case we find only four discrete maps: the trivial one, a Z 2 map dΦ → –dΦ, a Τ-duality-like map dΦ → i • dΦ, and the product of the last two.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Interacting chiral form field theories and $$ T\overline{T} $$-like flows in six and higher dimensions

Abstract In this paper we initiate the study of six-dimensional non-linear chiral two-form gauge theories as deformations of free chiral two-form gauge theories driven by stress-tensor$$ T\overline{T} $$ T T ¯ -like flows. To lay the background for this study, we elaborate on the relationship between different Lagrangian formulations of duality-invariantp-form theories and corresponding$$ T\overline{T} $$ T T ¯ -like flows in various dimensions. To this end we propose a new formulation which (i) is a generalization of the four-dimensional construction by Ivanov, Nurmagambetov and Zupnik (INZ) and (ii) turns into the PST formulation upon integrating out an auxiliary self-dual field. We elucidate space-time covariant properties of the PST formulation by clarifying and making use of its relation to the INZ-type formulation and to a so-called “clone” construction.

Physics↗

DOE OSTI2023

Spinor-helicity formalism for massive and massless amplitudes in five dimensions

Five-dimensional gauge and gravity theories are known to exhibit striking properties. D = 5 is the lowest dimension where massive tensor states appear naturally, providing a testing ground for perturbative insights into six-dimensional tensor theories. Five-dimensional supergravities are highly constrained and admit elegant geometric and algebraic formulations, with global symmetries manifest at the Lagrangian level. In this paper, we take a step towards the systematic investigation of amplitudes in five dimensions, and present a five-dimensional version of the spinor-helicity formalism, applicable to massless, massive and supersymmetric states. We give explicit representations for on-shell spinor and polarization variables such that the little-group symmetry and gauge redundancy are manifest. Massive self-dual tensor states are discussed in some detail, as well as all the on-shell supermultiplets that can appear in matter-coupled gauge and supergravity theories. As a byproduct of considering supersymmetry in the presence of central charge, we obtain massless ten-dimensional Majorana-Weyl spinors as products of five-dimensional massive spinors. We present compact expressions for superamplitudes at multiplicity three and four, including several novel superamplitudes that either do not straightforwardly uplift to six dimensions, or have not appeared in the six-dimensional literature. We discuss several examples of five-dimensional double-copy constructions in the context of gravitational theories with massive vectors and tensors, illustrating that the formalism we construct can also be used to considerably streamline the double-copy construction of $\mathcal{N}$ = 2 Maxwell-Einstein supergravities.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Flows in the space of interacting chiral boson theories

We study interacting theories of N left-moving and N ¯ right-moving Floreanini-Jackiw bosons in two dimensions. A parametrized family of such theories is shown to enjoy (nonmanifest) Lorentz invariance if and only if its Lagrangian obeys a flow equation driven by a function of the energy-momentum tensor. We discuss the canonical quantization of such theories along classical stress tensor flows, focusing on the case of the root- T T ¯ deformation, where we obtain perturbative results for the deformed spectrum in a certain large-momentum limit. In the special case N = N ¯ , we consider the quantum effective action for the root- T T ¯ -deformed theory by expanding around a general classical background, and we find that the one-loop contribution vanishes for backgrounds with constant scalar gradients. Our analysis can also be interpreted via dual U ( 1 ) Chern-Simons theories in three dimensions, which might be used to describe deformations of charged AdS 3 black holes or quantum Hall systems. Published by the American Physical Society 2024

Ebert, Stephen (ORCID:0000000154670155)↗

DOE OSTI2021

Truncation effects in the charge representation of the O(2) model

The O(2) model in Euclidean space-time is the zero-gauge-coupling limit of the compact scalar quantum electrodynamics. In this work, we obtain a dual representation of it called the charge representation. We study the quantum phase transition in the charge representation with a truncation to “spin $\textit{S}$," where the quantum numbers have an absolute value less than or equal to $\textit{S}$. The charge representation preserves the gapless-to-gapped phase transition even for the smallest spin truncation $\textit{S}$ = 1. The phase transition for $\textit{S}$ = 1 is an infinite-order Gaussian transition with the same critical exponents $\textit{δ}$ and $\textit{η}$ as the Berezinskii-Kosterlitz-Thouless (BKT) transition, while there are true BKT transitions for $\textit{S}$ ≥ 2 . The essential singularity in the correlation length for $\textit{S}$ = 1 is different from that for $\textit{S}$ ≥ 2 . The exponential convergence of the phase-transition point is studied in both Lagrangian and Hamiltonian formulations. We discuss the effects of replacing the truncated $\hat{U}^±$ = exp ($± i\hat{θ}$) operators by the spin ladder operators $\hat{S}^±$ in the Hamiltonian. The marginal operators vanish at the Gaussian transition point for $\textit{S}$ = 1, which allows us to extract the $\textit{η}$ exponent with high accuracy.

36 MATERIALS SCIENCE↗