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Results for “complementarity constraints”

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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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

On optimal control of hybrid dynamical systems using complementarity constraints

Optimal control for switch-based dynamical systems is a challenging problem in the process control literature. In this study, we model these systems as hybrid dynamical systems with finite number of unknown switching points and reformulate them using non-smooth and non-convex complementarity constraints as a mathematical program with complementarity constraints (MPCC). We utilize a moving finite element based strategy to discretize the differential equation system to accurately locate the unknown switching points at the finite element boundary and achieve high-order accuracy at intermediate non-collocation points. We propose a globalization approach to solve the discretized MPCC problem using a mixed NLP/MILP-based strategy to converge to a non-spurious first-order optimal solution. The method is tested on three dynamic optimization examples, including a gas–liquid tank model and an optimal control problem with a sliding mode solution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Modeling design and control problems involving neural network surrogates

Here, we consider nonlinear optimization problems that involve surrogate models represented by neural networks. We demonstrate first how to directly embed neural network evaluation into optimization models, highlight a difficulty with this approach that can prevent convergence, and then characterize stationarity of such models. We then present two alternative formulations of these problems in the specific case of feedforward neural networks with ReLU activation: as a mixed-integer optimization problem and as a mathematical program with complementarity constraints. For the latter formulation we prove that stationarity at a point for this problem corresponds to stationarity of the embedded formulation. Each of these formulations may be solved with state-of-the-art optimization methods, and we show how to obtain good initial feasible solutions for these methods. We compare our formulations on three practical applications arising in the design and control of combustion engines, in the generation of adversarial attacks on classifier networks, and in the determination of optimal flows in an oil well network.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A complementarity-based vapor-liquid equilibrium formulation for equation-oriented simulation and optimization

Vapor-Liquid Equilibrium (VLE) is a cornerstone of computer aided process engineering (CAPE). Embedded within process system models, VLE calculations are inherently procedural with non-smooth behavior that frequently require discrete decisions. Traditionally, these features resist the incorporation of VLE within efficient, large-scale equation-oriented (EO) process simulation and optimization strategies. On the other hand, recent reformulation of VLE models through the incorporation of complementarity constraints has broadened its scope to deal seamlessly with phase transitions and even supercritical excursions in process simulation and optimization. In this study, we extend these VLE complementarity models to EO frameworks where procedural thermodynamic property libraries are still required. Here, we develop an efficient, non-intrusive, and intuitive “square-flash” equation system that has been implemented within the IDAES Integrated Platform (IDAES-IP). Further, the effectiveness of this modular approach is demonstrated on case studies for non-ideal flash calculations and distillation optimization with disappearing phases and supercritical transitions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Implementing a unified solver for nonlinearly constrained optimization

SQP and interior-point methods (also referred to as Lagrange-Newton methods) typically share key algorithmic components, such as strategies for computing descent directions and mechanisms that promote global convergence. Building on this insight, we introduce a unifying framework with eight building blocks that abstracts the workflows of Lagrange-Newton methods. We then present Uno, a modular C++ solver that implements our unifying framework and allows the automatic combination of a wide range of strategies with no programming effort from the user. Uno is meant to (1) organize mathematical optimization strategies into a coherent hierarchy; (2) offer a wide range of efficient and robust methods that can be compared for a given instance; (3) enable researchers to experiment with novel optimization strategies; and (4) reduce the cost of development and maintenance of multiple optimization solvers. Uno’s software design allows user to compose new customized solvers for emerging optimization areas such as robust optimization or optimization problems with complementarity constraints, while building on reliable nonlinear optimization techniques. We demonstrate that Uno is highly competitive against state-of-the-art solvers filterSQP, IPOPT, SNOPT, MINOS, LANCELOT, LOQO, and CONOPT on a subset of 429 small problems from the CUTE collection. Uno is available as open-source software under the MIT license at https://github.com/cvanaret/Uno and via its C, Julia, Python, Fortran, and AMPL interfaces.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A Surrogate-Based Asynchronous Decomposition Technique for Realistic Security-Constrained Optimal Power Flow Problems

Here we present a decomposition approach for obtaining good feasible solutions for the security-constrained, alternating-current, optimal power flow (SC-AC-OPF) problem at an industrial scale and under real-world time and computational limits. The approach was designed while preparing and participating in ARPA-E’s Grid Optimization Competition (GOC) Challenge 1. The challenge focused on a near-real-time version of the SC-AC-OPF problem, where a base operating point is optimized, taking into account possible single-element contingencies, after which the system adapts its operating point following the response of automatic frequency droop controllers and voltage regulators. Our solution approach for this problem relies on state-of-the-art nonlinear programming algorithms, and it employs nonconvex relaxations for complementarity constraints, a specialized two-stage decomposition technique with sparse approximations of recourse terms and contingency ranking and prescreening. The paper describes and justifies our approach and outlines the features of its implementation, including functions and derivatives evaluation, warm-starting strategies, and asynchronous parallelism. We discuss the results of the independent benchmark of our approach by ARPA-E’s GOC team in Challenge 1, where it was found to consistently produce high-quality solutions across a wide range of network sizes and difficulty, and conclude by outlining future extensions of the approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Recent Developments in Security-Constrained AC Optimal Power Flow: Overview of Challenge 1 in the ARPA-E Grid Optimization Competition

In “Recent Developments in Security-Constrained AC Optimal Power Flow: Overview of Challenge 1 in the ARPA-E Grid Optimization Competition,” we review the state of the art in practical algorithms for scheduling power-systems operations in the short term and the results of the recent competition organized by the U.S. Advanced Research Projects Agency–Energy. We explain the mixed-integer nonlinear formulation used in the competition for nonspecialists in electrical engineering, the context and organization of the competition, and the performance of competitors. We find that the collective approaches and results of competitors provide support for efforts to move nonlinear optimization techniques into industrial applications, as they have proven to be a robust and efficient alternative to current linear approximation techniques.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Tidal disruption events and dark matter scatterings with neutrinos and photons

Stars can be tidally disrupted when passing near a black hole, and the debris can induce a flux of high-energy neutrinos. It has been discussed that there are hints in IceCube data of high-energy neutrinos produced in Tidal Disruption Events. The emitting region of neutrinos and photons in these astrophysical events is likely to be located in the vicinity of the central black hole, where the dark matter density might be significantly larger than in the outer regions of the galaxy. We explore the potential attenuation of the emitted neutrino and photon fluxes due to interactions with dark matter particles around the supermassive black hole of the host galaxies of AT2019dsg, AT2019fdr and AT2019aalc, and study the implications for some well-motivated models of dark matter-neutrino and dark matter-photon interactions. Furthermore, we discuss the complementarity of our constraints with values of the dark matter-neutrino scattering cross section proven to alleviate some cosmological tensions.

Fujiwara, Motoko↗
DOE OSTI2024

Combination of searches for heavy spin-1 resonances using 139 fb -1 of proton-proton collision data at $\sqrt{s}$ = 13 TeV with the ATLAS detector

A combination of searches for new heavy spin-1 resonances decaying into different pairings of W, Z, or Higgs bosons, as well as directly into leptons or quarks, is presented. The data sample used corresponds to 139 fb -1 of proton-proton collisions at $\sqrt{s}$ = 13 TeV collected during 2015–2018 with the ATLAS detector at the CERN Large Hadron Collider. Analyses selecting quark pairs (qq, bb, $t\overline{t}$, and tb) or third-generation leptons (τν and ττ) are included in this kind of combination for the first time. A simplified model predicting a spin-1 heavy vector-boson triplet is used. Cross-section limits are set at the 95% confidence level and are compared with predictions for the benchmark model. These limits are also expressed in terms of constraints on couplings of the heavy vector-boson triplet to quarks, leptons, and the Higgs boson. The complementarity of the various analyses increases the sensitivity to new physics, and the resulting constraints are stronger than those from any individual analysis considered. The data exclude a heavy vector-boson triplet with mass below 5.8 TeV in a weakly coupled scenario, below 4.4 TeV in a strongly coupled scenario, and up to 1.5 TeV in the case of production via vector-boson fusion.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS2012

Minimal Coordinate Formulation of Contact Dynamics in Operational Space

In recent years, complementarity techniques have been developed for modeling non-smooth contact and collision dynamics problems for multi-link robotic systems. Normally, in this approach, a linear complementarity problem (LCP) is set up using 6n non-minimal coordinates for a system with n links together with all the unilateral constraints and inter-link bilateral constraints on the system. In this paper, we use operational space dynamics to develop a complementarity formulation for contact and collision dynamics that uses minimal coordinates. The use of such non-redundant coordinates results in much smaller size LCP problems and the automatic enforcement of the inter-link bilateral constraints. Furthermore, we exploit operational space low-order computational algorithms to overcome some of the bottlenecks in using minimal coordinates.

contact dynamics↗
DOE OSTI2025

The electroweak precision constraints of the 2HDM+S

The 2HDM+S is the singlet extension of the Two-Higgs-Doublets Model (2HDM). The singlet field and its mixing with the 2HDM Higgs sector lead to new contributions to the electroweak precision observables, in particular, the oblique parameters. In this paper, we performed a systematic study of the impacts of each mixing angle to the oblique parameters. We adopted the mixing angles and physical Higgs masses as our parameters, which allows a mapping when specific symmetry structure of the Higgs potential and various theoretical considerations are taken into account. We identify five benchmark cases, where at most one mixing angle is nonzero and analyze the 95\% C.L. allowed parameter space by the oblique parameters. In the alignment limit of the 2HDM, we find that other than the usual mass relations of $m_H\sim m_{H^\pm}$ or $m_A\sim m_{H^\pm}$, electroweak precision measurements also impose an upper limit on the neutral Higgs masses. In the cases with nonzero singlet mixing with the 2HDM Higgses $H$ or $A$, we find approximate mass relations of $c^2_{\alpha_{HS}} m_{H} + s^2_{\alpha_{HS}}m_{h_S} = m_{H^\pm}$ or $c^2_{\alpha_{AS}} m_{A} + s^2_{\alpha_{AS}}m_{A_S} = m_{H^\pm}$. Those relations are universal to the 2HDM+S models, with or without further symmetry assumption. We also study the non-alignment limit of the 2HDM+S, which typically has tighter constraints on the masses and mixing angles. At the end, we examine the complementarity between the electroweak precision analyses and the Higgs coupling precision measurements.

2HDM↗
DOE OSTI2024

Cosmology with persistent homology: a Fisher forecast

Abstract Persistent homology naturally addresses the multi-scale topological characteristics of the large-scale structure as a distribution of clusters, loops, and voids. We apply this tool to the dark matter halo catalogs from theQuijotesimulations, and build a summary statistic for comparison with the joint power spectrum and bispectrum statistic regarding their information content on cosmological parameters and primordial non-Gaussianity. Through a Fisher analysis, we find that constraints from persistent homology are tighter for 8 out of the 10 parameters by margins of 13–50%. The complementarity of the two statistics breaks parameter degeneracies, allowing for a further gain in constraining power when combined. We run a series of consistency checks to consolidate our results, and conclude that our findings motivate incorporating persistent homology into inference pipelines for cosmological survey data.

Astronomy & Astrophysics↗
DOE OSTI2023

An Incremental Gradient Method for Optimization Problems With Variational Inequality Constraints

We consider minimizing a sum of agent-specific nondifferentiable merely convex functions over the solution set of a variational inequality (VI) problem in that each agent is associated with a local monotone mapping. This problem finds an application in computation of the best equilibrium in nonlinear complementarity problems arising in transportation networks. We develop an iteratively regularized incremental gradient method where at each iteration, agents communicate over a directed cycle graph to update their solution iterates using their local information about the objective and the mapping. The proposed method is single-timescale in the sense that it does not involve any excessive hard-to-project computation per iteration. We derive nonasymptotic agent-wise convergence rates for the suboptimality of the global objective function and infeasibility of the VI constraints measured by a suitably defined dual gap function. Finally, the proposed method appears to be the first fully iterative scheme equipped with iteration complexity that can address distributed optimization problems with VI constraints over cycle graphs.

convergence↗
DOE OSTI2023

Probing lepton flavor violation at Circular Electron-Positron Colliders

Lepton flavor violation is one of the cleanest probes of physics beyond the standard model. In this work, we explore the sensitivity of the process e + e – → τμ to new physics above the TeV scale at the proposed circular electron-positron colliders FCC-ee and CEPC. We compute the e + e – → τμ cross-section in the Standard Model Effective Field Theory and assess the relevant backgrounds. We compare our sensitivity projections to existing and expected constraints from tau decays and Z decays and find that the future electron-positron colliders provide competitive probes of new physics. We highlight the complementarity of searches for resonant e + e – → Z → τμ production on the Z pole and searches for non-resonant e + e – → τμ at higher center-of-mass energies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Forecasting dark showers at Belle II

Dark showers from strongly interacting dark sectors that confine at the GeV scale can give rise to novel signatures at e + e - colliders. In this work, we study the sensitivity of B factory experiments to dark showers produced through an effective interaction arising from a heavy off-shell mediator. We show that a prospective search for displaced vertices from GeV-scale long-lived particles at Belle II can improve the sensitivity to dark showers substantially compared to an existing search at BaBar. We compare the sensitivity of searches for displaced signals to searches for promptly produced resonances at BaBar and KLOE and calculate sensitivity projections for a single-photon search at Belle II to invisible dark showers produced through an effective interaction. The underlying structure of the effective interaction can be resolved at higher-energy experiments, where the mediator can be produced on-shell. To study the resulting constraints, we update electroweak precision bounds on kinetically mixed Z' bosons and reinterpret a search for low-mass di-muon resonances at LHCb in terms of dark showers. We find that LHCb and Belle II are most sensitive to different particle decay lengths, underscoring the complementarity of LHC and intensity frontier experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Top-down design of protein architectures with reinforcement learning

As a result of evolutionary selection, the subunits of naturally occurring protein assemblies often fit together with substantial shape complementarity to generate architectures optimal for function in a manner not achievable by current design approaches. We describe a “top-down” reinforcement learning–based design approach that solves this problem using Monte Carlo tree search to sample protein conformers in the context of an overall architecture and specified functional constraints. Cryo–electron microscopy structures of the designed disk-shaped nanopores and ultracompact icosahedra are very close to the computational models. The icosohedra enable very-high-density display of immunogens and signaling molecules, which potentiates vaccine response and angiogenesis induction. Our approach enables the top-down design of complex protein nanomaterials with desired system properties and demonstrates the power of reinforcement learning in protein design.

Science & Technology - Other Topics↗
DOE OSTI2025

Constraining non-standard neutrino interactions with neutral current events at long-baseline oscillation experiments

We explore, for the first time, neutral-curren t events at long-baseline experiments to constrain vector and axial-vector neutrino non-standard interactions (NSI) with quarks. We leverage the flavor dependence of NSIs to perform an oscillation analysis in the neutral- current channel. We first introduce a framework to parametrize the effect of NSI on the cross section. Then, as an example, we analyze NOvA neutral-current data which provides significantly improved constraints on the axial-vector NSI parameters ${\varepsilon}_{\mu \mu}^A$, ${\varepsilon}_{\tau \tau}^A$ and ${\varepsilon}_{e\mu}^A$. This is highly complementary to constraints from SNO data, which, differently from long-baseline neutral current data, is not sensitive to isospin conserving NSIs ${\varepsilon}_u^A$ = ${\varepsilon}_d^A$. Additionally, we disfavor large values of the diagonal vectorial NSI ${\varepsilon}_{\mu \mu}^{VV}$ and ${\varepsilon}_{\tau \tau}^V$ which originate from the LMA-Dark solution. We also highlight the complementarity between NSI searches at oscillation experiments using charged current and neutral current channels.

neutrino interactions↗
DOE OSTI2025

Constraining non-standard neutrino interactions with neutral current events at long-baseline oscillation experiments

We explore, for the first time, neutral-current events at long-baseline experiments to constrain vector and axial-vector neutrino non-standard interactions (NSI) with quarks. We leverage the flavor dependence of NSIs to perform an oscillation analysis in the neutral- current channel. We first introduce a framework to parametrize the effect of NSI on the cross section. Then, as an example, we analyze NOvA neutral-current data which provides significantly improved constraints on the axial-vector NSI parameters $ {\varepsilon}_{\mu \mu}^A $,$ {\varepsilon}_{\tau \tau}^A $ and $ {\varepsilon}_{e\mu}^A $. This is highly complementary to constraints from SNO data, which, differently from long-baseline neutral current data, is not sensitive to isospin conserving NSIs $ {\varepsilon}_u^A $ = $ {\varepsilon}_d^A $. Additionally, we disfavor large values of the diagonal vectorial NSI $ {\varepsilon}_{\mu \mu}^{VV} $ and $ {\varepsilon}_{\tau \tau}^V $ which originate from the LMA-Dark solution. We also highlight the complementarity between NSI searches at oscillation experiments using charged current and neutral current channels.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Dynamical dark energy in light of the DESI DR2 baryonic acoustic oscillations measurements

Understanding whether cosmic acceleration arises from a cosmological constant or a dynamical component is a central goal of cosmology, and the Dark Energy Spectroscopic Instrument (DESI) enables stringent tests with high-precision distance measurements. Here we analyse measurements of baryon acoustic oscillations in DESI Data Release 1 and Data Release 2 and consider type Ia supernovae and a distance prior for the cosmic microwave background. With the larger statistical power and wider redshift coverage of Data Release 2, the preference for dynamical dark energy does not diminish relative to Data Release 1. Using both a shape-function reconstruction and non-parametric approaches with a Horndeski-motivated correlation prior, we find that the equation of state for dark energy w(z) varies with redshift. Baryon acoustic oscillation data alone yield modest constraints, but in combination with independent supernova compilations and the prior for the cosmic microwave background, they strengthen the evidence for dynamics. A Bayesian comparison of models shows moderate support for departures from Λ cold dark matter (ΛCDM) when several degrees of freedom in w(z) are allowed, corresponding to ~3σ tension with ΛCDM (and higher for some datasets). Despite methodological differences, our results are consistent with companion DESI papers, underscoring the complementarity of the approaches. Possible systematics remain under study; forthcoming DESI, Euclid and next-generation cosmic microwave background data will provide decisive tests.

cosmology↗