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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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DOE OSTI2018

A family of second-order fully explicit time integration schemes

A new family of fully explicit time integration methods is proposed, which has second-order accuracy for structures with and without damping. Using a diagonal mass matrix, the suggested scheme remains fully explicit not only for structures with a non-diagonal damping matrix, but also when the internal force vector is a nonlinear function of velocity. The present algorithm has an acceptable domain of stability, and it is self-starting. This technique introduces effectively numerical dissipation to suppress the high-frequency spurious modes, while at the same time the lower modes are not affected too much. In addition, numerical dispersion error of the scheme is considerably smaller than that of the central difference method. Solving several linear and nonlinear problems highlights the superior performance of the authors’ approach. Findings demonstrate that solution time for the suggested scheme is much less than that of the central difference technique. The related algorithm can be easily implemented into programs, which already contain the central difference method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Incorporation of market signals for the optimal design of post combustion carbon capture systems

Recent studies have shown that fossil generators equipped with post-combustion carbon capture (PCC) systems are needed to reduce the cost of deep decarbonization. Such generators need to be flexible and responsive to grid conditions, particularly in a high variable renewable energy (VRE) environment. In this work, we evaluate the net present value (NPV) of retrofitting an existing natural gas combined cycle (NGCC) unit with a flexible PCC system while incorporating market signals from a high VRE grid. We use our industrial partner’s NGCC configuration as representative of existing NGCC units and Svante’s rapid-temperature swing adsorption (TSA) for PCC. Because of its ability to rapidly startup/shutdown and ramp-up/ramp-down, the chosen capture technology is very attractive for load-following operations. For a given set of market signals, we formulate a two-stage stochastic multi-period optimization problem, under the price-taker assumption, to simultaneously optimize the design of the capture system and operation of the entire plant. Rigorous models for the NGCC unit, PCC system, and compression system are developed using commercial process simulators and validated with either plant or vendor data. For computational tractability, we develop surrogate/reduced-order models for use in the optimization problem. The surrogate model for the NGCC plant is constructed by linearizing the rigorous dynamic model at 75% load, while data-driven nonlinear surrogate models for the capture and compression systems are constructed using simulation data from the rigorous models. The optimization problem, formulated as a mixed integer bilinear program, is implemented in the IDAES® integrated platform and solved to global optimality using Gurobi 9.5. Using this formulation, we determine the profitability of retrofitting an existing NGCC unit with the chosen capture system for multiple regions in the U.S. under two scenarios with different carbon prices. Importantly, the results show that the optimal decision strongly depends on the region and on the carbon price, thereby demonstrating the importance of the inclusion of market signals in the design process.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2014

On the robust optimization to the uncertain vaccination strategy problem

In order to prevent an epidemic of infectious diseases, the vaccination coverage needs to be minimized and also the basic reproduction number needs to be maintained below 1. This means that as we get the vaccination coverage as minimum as possible, thus we need to prevent the epidemic to a small number of people who already get infected. In this paper, we discuss the case of vaccination strategy in term of minimizing vaccination coverage, when the basic reproduction number is assumed as an uncertain parameter that lies between 0 and 1. We refer to the linear optimization model for vaccination strategy that propose by Becker and Starrzak (see [2]). Assuming that there is parameter uncertainty involved, we can see Tanner et al (see [9]) who propose the optimal solution of the problem using stochastic programming. In this paper we discuss an alternative way of optimizing the uncertain vaccination strategy using Robust Optimization (see [3]). In this approach we assume that the parameter uncertainty lies within an ellipsoidal uncertainty set such that we can claim that the obtained result will be achieved in a polynomial time algorithm (as it is guaranteed by the RO methodology). The robust counterpart model is presented.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2014

MO-PIS-Exhibit Hall-01: Tools for TG-142 Linac Imaging QA I

Partners in Solutions is an exciting new program in which AAPM partners with our vendors to present practical “hands-on” information about the equipment and software systems that we use in our clinics. The therapy topic this year is solutions for TG-142 recommendations for linear accelerator imaging QA. Note that the sessions are being held in a special purpose room built on the Exhibit Hall Floor, to encourage further interaction with the vendors. Automated Imaging QA for TG-142 with RIT Presentation Time: 2:45 – 3:15 PM This presentation will discuss software tools for automated imaging QA and phantom analysis for TG-142. All modalities used in radiation oncology will be discussed, including CBCT, planar kV imaging, planar MV imaging, and imaging and treatment coordinate coincidence. Vendor supplied phantoms as well as a variety of third-party phantoms will be shown, along with appropriate analyses, proper phantom setup procedures and scanning settings, and a discussion of image quality metrics. Tools for process automation will be discussed which include: RIT Cognition (machine learning for phantom image identification), RIT Cerberus (automated file system monitoring and searching), and RunQueueC (batch processing of multiple images). In addition to phantom analysis, tools for statistical tracking, trending, and reporting will be discussed. This discussion will include an introduction to statistical process control, a valuable tool in analyzing data and determining appropriate tolerances. An Introduction to TG-142 Imaging QA Using Standard Imaging Products Presentation Time: 3:15 – 3:45 PM Medical Physicists want to understand the logic behind TG-142 Imaging QA. What is often missing is a firm understanding of the connections between the EPID and OBI phantom imaging, the software “algorithms” that calculate the QA metrics, the establishment of baselines, and the analysis and interpretation of the results. The goal of our brief presentation will be to establish and solidify these connections. Our talk will be motivated by the Standard Imaging, Inc. phantom and software solutions. We will present and explain each of the image quality metrics in TG-142 in terms of the theory, mathematics, and algorithms used to implement them in the Standard Imaging PIPSpro software. In the process, we will identify the regions of phantom images that are analyzed by each algorithm. We then will discuss the process of the creation of baselines and typical ranges of acceptable values for each imaging quality metric.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2014

WE-PIS-Exhibit Hall-01: Tools for TG-142 Linac Imaging QA II

Partners in Solutions is an exciting new program in which AAPM partners with our vendors to present practical “hands-on” information about the equipment and software systems that we use in our clinics. The therapy topic this year is solutions for TG-142 recommendations for linear accelerator imaging QA. Note that the sessions are being held in a special purpose room built on the Exhibit Hall Floor, to encourage further interaction with the vendors. Using DoseLab to Perform TG-142 Imaging QA The goals of this session will be to present a clinical overview of acquiring images for TG-142 Imaging QA, as well as analyzing and evaluating results using DoseLab software. DoseLab supports planar imaging QA analysis using almost any QA phantom provided by numerous vendors. General advantages and disadvantages of selecting each of these phantoms will be briefly summarized. Best practices for selecting image acquisition parameters will be presented. A demonstration of using DoseLab software to perform a series of TG-142 tests will be performed. We will disuss why DoseLab uses its own set of imaging QA formulas, and why imaging QA measurement values of the same nominal properties will vary between TG- 142 software packages. Because TG-142 does not specify baseline and tolerance values for imaging QA, the presentation will recommend performing the manufacturer's acceptance test procedure to validate the equipment is functioning correctly. Afterwards, results can be obtained using the clinic's selected set of phantoms, image acquisition parameters, and TG-142 software to set proper baseline values. This presentation will highlight the reasons why comparing imaging QA results can be trickier than comparing linear accelerator treatment results and what physicists should keep in mind when comparing imaging QA results for different machines. Physicists are often unsure of the next step when there is an issue discovered during Imaging QA. Therefore, a few common examples of imaging issues and recommended solutions will be discussed. TG-142 Imaging QA Simplified: Lessons From Diagnostic Physics Collaboration There are many commercial options for the performance of imaging quality assurance tests for the linear accelerator imaging systems as required by the AAPM TG-142 report. Imaging quality assurance testing is largely performed by the diagnostic physicist so routine performance of these tests by the practicing oncology physicist can be complicated and confusing given all of the commercially available options. This presentation focuses on the performance of imaging quality assurance testing for linear accelerators using methods similar to that of diagnostic physicists. This presentation will address the ability to perform the required testing without complicated software and explores solutions for the performance of these tests in an efficient manner while still maintaining the ability to ascertain image quality changes that may ultimately affect clinical decisions.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2017

Interior Lighting Campaign Adds Luminaire Categories; Announces 2018 Recognition Event

This article will be published in the November issue of the International Facility Management Association's sustainability newsletter. The article both informs facility managers of the Interior Lighting Campaign, and invites them to participate. Highlights include the new types of lamps recently included along with program details.

Energy Efficiency↗
DOE OSTI2024

MolSym : A Python package for handling symmetry in molecular quantum chemistry

A consideration of the point group symmetry of molecules is often advantageous from a computational efficiency standpoint and sometimes necessary for the correct treatment of chemical physics problems. Many modern electronic structure software packages include a treatment of symmetry, but these are sometimes incomplete or unusable outside of that program’s environment. Therefore, we have developed the MolSym package for handling molecular symmetry and its associated functionalities to provide a platform for including symmetry in the implementation and development of other methods. Features include point group detection, molecule symmetrization, arbitrary generation of symmetry element sets and character tables, and symmetry adapted linear combinations of real spherical harmonic basis functions, Cartesian displacement coordinates, and internal coordinates. We present some of the advantages of using molecular symmetry as achieved by MolSym, particularly with respect to Hartree–Fock theory, and the reduction of finite difference displacements in gradient/Hessian computations. Furthermore, this package is designed to be easily integrated into other software development efforts and may be extended to further symmetry applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

WE-AB-BRB-06: A Temperature Independent Plastic Scintillation Detector Capable of Simultaneous Dose and Temperature Measurement

Purpose: To evaluate a measurement method that renders plastic scintillation detectors temperature independent and capable of recovering dose and temperature information simultaneously. Methods: A novel approach was developed to account for the temperature dependence of plastic scintillation detectors (PSDs) without prior knowledge of the temperature. To enable this, the optical response of the scintillating element is separated into two sub-components, one being the response at a given temperature and the other accounting for the change in the optical emission spectrum with temperature. Using a previously demonstrated hyperspectral approach and following the proper calibration protocol, the contribution to scintillator emission and physical value of both dose and temperature can be obtained in real-time. To validate the method, dose and temperature were measured under cobalt irradiation in a temperature controlled water tank developed for this study. The temperature was varied from 22°C to 42°C. Depth-dose curves were also obtained during irradiations from a linear accelerator, first maintaining the water at room temperature and then warming it to 40°C and letting it cool down naturally over the course of the second measurement. Results: Dose measurements delivered with the Co-60 unit showed an average relative difference to the expected value of (1.0±0.8)%, with a maximum difference of 2.3% over the entire range of temperatures. The measured temperatures using the PSD were all within 1°C of the expected values. The difference between room temperature and warmer depth dose measurements differed by only (1.2±0.4)%. The dosimeter showed to be accurate for temporal resolution down to 0.1s. Conclusion: The proposed method was shown to reliably correct for the temperature dependence of a PSD. Additionally, it makes it possible to assess the temperature at the point of measurement. These are significant advances in PSD technology, particularly in relation to real-time in vivo dosimetry. Part of this research was supported by the Odyssey Program at The University of Texas MD Anderson Cancer Center.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

Mathematical solutions in internal dose assessment: A comparison of Python-based differential equation solvers in biokinetic modeling

Abstract In biokinetic modeling systems employed for radiation protection, biological retention and excretion have been modeled as a series of discretized compartments representing the organs and tissues of the human body. Fractional retention and excretion in these organ and tissue systems have been mathematically governed by a series of coupled first-order ordinary differential equations (ODEs). The coupled ODE systems comprising the biokinetic models are usually stiff due to the severe difference between rapid and slow transfers between compartments. In this study, the capabilities of solving a complex coupled system of ODEs for biokinetic modeling were evaluated by comparing different Python programming language solvers and solving methods with the motivation of establishing a framework that enables multi-level analysis. The stability of the solvers was analyzed to select the best performers for solving the biokinetic problems. A Python-based linear algebraic method was also explored to examine how the numerical methods deviated from an analytical or semi-analytical method. Results demonstrated that customized implicit methods resulted in an enhanced stable solution for the inhaled 60 Co (Type M) and 131 I (Type F) exposure scenarios for the inhalation pathway of the International Commission on Radiological Protection (ICRP) Publication 130 Human Respiratory Tract Model (HRTM). The customized implementation of the Python-based implicit solvers resulted in approximately consistent solutions with the Python-based matrix exponential method ( expm ). The differences generally observed between the implicit solvers and expm are attributable to numerical precision and the order of numerical approximation of the numerical solvers. This study provides the first analysis of a list of Python ODE solvers and methods by comparing their usage for solving biokinetic models using the ICRP Publication 130 HRTM and provides a framework for the selection of the most appropriate ODE solvers and methods in Python language to implement for modeling the distribution of internal radioactivity.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2021

Decentralized Low-Rank State Estimation for Power Distribution Systems

This article considers the low-observability state estimation problem in power distribution networks and develops a decentralized state estimation algorithm leveraging the matrix completion methodology. Matrix completion has been shown to be an effective technique in state estimation that exploits the low dimensionality of the power system measurements to recover missing information. This technique can utilize an approximate (linear) load flow model, or it can be used with no physical models in a network where no information about the topology or line admittance is available. The direct application of matrix completion algorithms requires solving a semi-definite programming (SDP) problem, which becomes computationally challenging for large networks. We therefore develop a decentralized algorithm that capitalizes on the popular proximal alternating direction method of multipliers (proximal ADMM). The method allows us to distribute the computation among different areas of the network, leading to a scalable algorithm. By doing all computations at individual control areas and only communicating with neighboring areas, the algorithm eliminates the need for data to be sent to a central processing unit and thus increases efficiency and contributes to the goal of autonomous control of distribution networks. We illustrate the advantages of the proposed algorithm numerically using standard IEEE test cases.

41 EE - Solar Energy Technologies Office (EE-4S)↗
DOE OSTI2017

Assimilation of Wave Imaging Radar Observations for Real-time Wave-by-Wave Forecasting

This project addressed Topic 3: “Wave Measurement Instrumentation for Feed Forward Controls” under the FOA number DE-FOA-0000971. The overall goal of the program was to develop a phase-resolving wave forecasting technique for application to the active control of Wave Energy Conversion (WEC) devices. We have developed an approach that couples a wave imaging marine radar with a phase-resolving linear wave model for real-time wave field reconstruction and forward propagation of the wave field in space and time. The scope of the project was to develop and assess the performance of this novel forecasting system. Specific project goals were as follows: Develop and verify a fast, GPU-based (Graphical Processing Unit) wave propagation model suitable for phase-resolved computation of nearshore wave transformation over variable bathymetry; Compare the accuracy and speed of performance of the wave model against a deep water model in their ability to predict wave field transformation in the intermediate water depths (50 to 70 m) typical of planned WEC sites; Develop and implement a variational assimilation algorithm that can ingest wave imaging radar observations and estimate the time-varying wave conditions offshore of the domain of interest such that the observed wave field is best reconstructed throughout the domain and then use this to produce model forecasts for a given WEC location; Collect wave-resolving marine radar data, along with relevant in situ wave data, at a suitable wave energy test site, apply the algorithm to the field data, assess performance, and identify any necessary improvements; and Develop a production cost estimate that addresses the affordability of the wave forecasting technology and include in the Final Report. The developed forecasting algorithm (“Wavecast”) was evaluated for both speed and accuracy against a substantial synthetic dataset. Early in the project, performance tests definitively demonstrated that the system was capable of forecasting in real-time, as the GPU-based wave model backbone was very computationally efficient. The data assimilation algorithm was developed on a polar grid domain in order to match the sampling characteristics of the observation system (wave imaging marine radar). For verification purposes, a substantial set of synthetic wave data (i.e. forward runs of the wave model) were generated to be used as ground truth for comparison to the reconstructions and forecasts produced by Wavecast. For these synthetic cases, Wavecast demonstrated very good accuracy, for example, typical forecast correlation coefficients were between 0.84-0.95 when compared to the input data. Dependencies on shadowing, observational noise, and forecast horizon were also identified. During the second year of the project, a short field deployment was conducted in order to assess forecast accuracy under field conditions. For this, a radar was installed on a fishing vessel and observations were collected at the South Energy Test Site (SETS) off the coast of Newport, OR. At the SETS site, simultaneous in situ wave observations were also available owing to an ongoing field project funded separately. Unfortunately, the position and heading information that was available for the fishing vessel were not of sufficient accuracy in order to validate the forecast in a phase-resolving sense. Instead, a spectral comparison was made between the Wavecast forecast and the data from the in situ wave buoy. Although the wave and wind conditions during the field test were complex, the comparison showed a promising reconstruction of the wave spectral shape, where both peaks in the bimodal spectrum were represented. However, the total reconstructed spectral energy (across all directions and frequencies) was limited to 44% of the observed spectrum. Overall, wave-by-wave forecasting using a data assimilation approach based on wave imaging radar observations and a physics-based wave model shows promise for short-term phase-resolved predictions. Two recommendations for future work are as follows: first, we would recommend additional focused field campaigns for algorithm validation. The field campaign should be long enough to capture a range of wave conditions relevant to the target application and WEC site. In addition, it will be crucial to make sure the vessel of choice has high accuracy position and heading instrumentation (this instrumentation is commercially available but not standard on commercial fishing vessels). The second recommendation is to expand the model physics in the wave model backbone to include some nonlinear effects. Specifically, the third-order correction to the wave speed due to amplitude dispersion would be the next step in order to more accurately represent the phase speeds of large amplitude waves.

16 TIDAL AND WAVE POWER↗
DOE OSTI2016

SU-G-BRB-02: An Open-Source Software Analysis Library for Linear Accelerator Quality Assurance

Purpose: Routine linac quality assurance (QA) tests have become complex enough to require automation of most test analyses. A new data analysis software library was built that allows physicists to automate routine linear accelerator quality assurance tests. The package is open source, code tested, and benchmarked. Methods: Images and data were generated on a TrueBeam linac for the following routine QA tests: VMAT, starshot, CBCT, machine logs, Winston Lutz, and picket fence. The analysis library was built using the general programming language Python. Each test was analyzed with the library algorithms and compared to manual measurements taken at the time of acquisition. Results: VMAT QA results agreed within 0.1% between the library and manual measurements. Machine logs (dynalogs & trajectory logs) were successfully parsed; mechanical axis positions were verified for accuracy and MLC fluence agreed well with EPID measurements. CBCT QA measurements were within 10 HU and 0.2mm where applicable. Winston Lutz isocenter size measurements were within 0.2mm of TrueBeam’s Machine Performance Check. Starshot analysis was within 0.2mm of the Winston Lutz results for the same conditions. Picket fence images with and without a known error showed that the library was capable of detecting MLC offsets within 0.02mm. Conclusion: A new routine QA software library has been benchmarked and is available for use by the community. The library is open-source and extensible for use in larger systems.

43 PARTICLE ACCELERATORS↗
DOE OSTI2023

A Sequential Quadratic Programming Algorithm for Nonsmooth Problems with Upper- \({\boldsymbol{\mathcal{C}^2}}\) Objective

An optimization algorithm for nonsmooth nonconvex constrained optimization problems with upper- \({\boldsymbol{\mathcal{C}^2}}\) objective functions is proposed and analyzed. Upper- \({\boldsymbol{\mathcal{C}^2}}\) is a weakly concave property that exists in difference of convex (DC) functions and arises naturally in many applications, particularly certain classes of solutions to parametric optimization problems e.g., recourse of stochastic programming and projection onto closed sets. The algorithm can be viewed as an extension of sequential quadratic programming (SQP) to nonsmooth problems with upper- \({\boldsymbol{\mathcal{C}^2}}\) objectives or a simplified bundle method. It is globally convergent with bounded algorithm parameters that are updated with a trust-region criterion. The algorithm handles general smooth constraints through linearization and uses a line search to ensure progress. The potential inconsistencies from the linearization of the constraints are addressed through a penalty method. In conclusion, the capabilities of the algorithm are demonstrated by solving both simple upper- \({\boldsymbol{\mathcal{C}^2}}\) problems and a real-world optimal power flow problem used in current power grid industry practices.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Alpha Radiolysis of Nuclear Solvent Extraction Ligands Used for An(III) and Ln(III) Separations

This document is the final report for the Nuclear Energy Universities Program (NEUP) grant 10-910 (DE-AC07-05ID14517) “Alpha Radiolysis of Nuclear Solvent Extraction Ligands used for An(III) and Ln(III) Separations”. The goal of this work was to obtain a quantitative understanding of the impacts of both low Linear Energy Transfer (LET, gamma-rays) and high LET (alpha particles) radiation chemistry occurring in future large-scale separations processes. This quantitative understanding of the major radiation effects on diluents and ligands is essential for optimal process implementation, and could result in significant cost savings in the future.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Th and U fuel photofission study by NTD for AD-MSR subcritical assembly

During the last decade a considerable effort has been devoted for developing energy generating systems based on advanced nuclear technology within the design concepts of GEN-IV. Thorium base fuel systems such as accelerator driven nuclear reactors are one of the often mentioned attractive and affordable options. Several radiotherapy linear accelerators are on the market and due to their reliability, they could be employed as drivers for subcritical liquid fuel assemblies. Bremsstrahlung photons with energies above 5.5MeV, induce (γ,n) and (e,e’n) reactions in the W-target. Resulting gamma radiation and photo or fission neutrons may be absorbed in target materials such as thorium and uranium isotopes to induce sustained fission or nuclear transmutation in waste radioactive materials. Relevant photo driven and photo-fission reaction cross sections are important for actinides {sup 232}Th, {sup 238}U and {sup 237}Np in the radiotherapy machines energy range of 10-20 MV. In this study we employ passive nuclear track detectors (NTD) to determine fission rates and neutron production rates with the aim to establish the feasibility for gamma and photo-neutron driven subcritical assemblies. To cope with these objectives a 20 MV radiotherapy machine has been employed with a mixed fuel target. Results will support further development for a subcritical assembly employing a thorium containing liquid fuel. It is expected that acquired technological knowledge will contribute to the Venezuelan nuclear energy program.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

BioXTAS RAW 2 : new developments for a free open-source program for small-angle scattering data reduction and analysis

BioXTAS RAW is a free open-source program for reduction, analysis and modelling of biological small-angle scattering data. Here, the new developments in RAW version 2 are described. These include improved data reduction using pyFAI ; updated automated Guinier fitting and D max finding algorithms; automated series ( e.g. size-exclusion chromatography coupled small-angle X-ray scattering or SEC-SAXS) buffer- and sample-region finding algorithms; linear and integral baseline correction for series; deconvolution of series data using regularized alternating least squares ( REGALS ); creation of electron-density reconstructions using electron density via solution scattering ( DENSS ); a comparison window showing residuals, ratios and statistical comparisons between profiles; and generation of PDF reports with summary plots and tables for all analysis. Furthermore, there is now a RAW API, which can be used without the graphical user interface (GUI), providing full access to all of the functionality found in the GUI. In addition to these new capabilities, RAW has undergone significant technical updates, such as adding Python 3 compatibility, and has entirely new documentation available both online and in the program.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

An effective description of charge diffusion and energy transport in a charged plasma from holography

We discuss the physics of sound propagation and charge diffusion in a plasma with non-vanishing charge density. Our analysis culminates the program initiated in to construct an open effective field theory of low-lying modes of the stress tensor and charge current in such plasmas. We model the plasma holographically as a Reissner-Nordström-AdS d+1 black hole, and study linearized fluctuations of longitudinally polarized scalar gravitons and photons in this background. We demonstrate that the perturbations can be decoupled and repackaged into the dynamics of two designer scalars, whose gravitational coupling is modulated by a non-trivial dilatonic factor. The holographic analysis allows us to isolate the phonon mode from the charge diffusion mode, and identify the combination of currents that corresponds to each of them. We use these results to obtain the real-time Gaussian effective action, which includes both the retarded response and the associated stochastic (Hawking) fluctuations, accurate to quartic order in gradients.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

Polyhedral approximation in mixed-integer convex optimization

Generalizing both mixed-integer linear optimization and convex optimization, mixed-integer convex optimization possesses broad modeling power but has seen relatively few advances in general-purpose solvers in recent years. Here, we intend to provide a broadly accessible introduction to our recent work in developing algorithms and software for this problem class. Our approach is based on constructing polyhedral outer approximations of the convex constraints, resulting in a global solution by solving a finite number of mixed-integer linear and continuous convex subproblems. The key advance we present is to strengthen the polyhedral approximations by constructing them in a higher-dimensional space. In order to automate this extended formulation we rely on the algebraic modeling technique of disciplined convex programming (DCP), and for generality and ease of implementation we use conic representations of the convex constraints. Although our framework requires a manual translation of existing models into DCP form, after performing this transformation on the MINLPLIB2 benchmark library we were able to solve a number of unsolved instances and on many other instances achieve superior performance compared with state-of-the-art solvers like Bonmin, SCIP, and Artelys Knitro.

97 MATHEMATICS AND COMPUTING↗