Search NASA⌕ Search

SEARCH · Search NASA

Results for “Convex optimization”

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.

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

At least 577 records · Page 32
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

On Nonuniqueness of Solutions of Hamilton–Jacobi–Bellman Equations

An example of a nonunique solution of the Cauchy problem of Hamilton–Jacobi–Bellman (HJB) equation with surprisingly regular Hamiltonian is presented. The Hamiltonian H(t, x, p) is locally Lipschitz continuous with respect to all variables, convex in p and with linear growth with respect to p and x. The HJB equation possesses two distinct lower semicontinuous solutions with the same final conditions; moreover, one of them is the value function of the corresponding Bolza problem. The definition of lower semicontinuous solution was proposed by Frankowska (SIAM J. Control Optim. 31:257–272, 1993) and Barron and Jensen (Commun. Partial Differ. Equ. 15(12):1713–1742, 1990). Using the example an analysis and comparison of assumptions in some uniqueness results in HJB equations is provided.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1997

Low-leakage and low-instability labyrinth seal

Improved labyrinth seal designs are disclosed. The present invention relates to labyrinth seal systems with selected sealing surfaces and seal geometry to optimize flow deflection and produce maximum turbulent action. Optimum seal performance is generally accomplished by providing sealing surfaces and fluid cavities formed to dissipate fluid energy as a function of the geometry of the sealing surfaces along with the position and size of the fluid cavities formed between members of the labyrinth seal system. Improved convex surfaces, annular flow reversal grooves, flow deflection blocks and rough, machined surfaces cooperate to enhance the performance of the labyrinth seal systems. For some labyrinth seal systems a mid-cavity throttle and either rigid teeth or flexible spring teeth may be included.

Rhode, David L.↗
DOE OSTI2016

A Generic Model for Electric Double Layers in Porous Electrodes

The performance of electric-double-layer capacitors (EDLCs) hinges on microscopic charge distributions near the electrode/electrolyte interfaces. Whereas practical EDLCs consist of electrodes made of amorphous porous materials, theoretical understanding of EDLCs is mostly based on EDL structure near a planar surface or on simplistic models that have little relevance to realistic systems. In this work, we propose a spherical shell model to account for both pore size and curvature effects of amorphous porous materials. The EDL structure in spherical shells has been investigated over a broad range of pore sizes and curvatures by use of classic density functional theory. Theoretical results reveal that the curvature effects on convex and concave EDLs are drastically different and that materials with extensive convex surfaces will lead to maximized capacitance. Like a slit pore, the spherical shell model also predicts oscillatory variation of capacitance with pore size, but the oscillatory behavior is magnified as the curvature increases. The joint effects of pore size and curvature identified in this work give new insight into materials design for porous electrodes with optimal EDLC performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

High-power terahertz quantum cascade lasers with ∼0.23 W in continuous wave mode

Terahertz quantum cascade lasers with a record output power up to ∼0.23 W in continuous wave mode were obtained. We show that the optimal 2.9-mm-long device operating at 3.11 THz has a low threshold current density of 270 A/cm{sup 2} at ∼15 K. The maximum operating temperature arrived at ∼65 K in continuous wave mode and the internal quantum efficiencies decreased from 0.53 to 0.19 for the devices with different cavity lengths. By using one convex lens with the effective focal length of 13 mm, the beam profile was collimated to be a quasi Gaussian distribution.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2020

Theoretical search for possible Li–Ni–B crystal structures using an adaptive genetic algorithm

The structural diversity of rare-earth and transition metal borides indicates that alkali-transition metal borides (A-T-B) show tremendous promise in exhibiting a variety of crystal structures with different dimensionalities of T-B frameworks. On the other hand, the A-T-B ternary systems are severely underexplored because of the synthetic challenges associated with their preparation. Accurate and efficient computational predictions of low-energy stable and metastable phases can identify the optimal compositions of the hypothetical compounds in the A-T-B systems to guide the synthesis. As such, in this work, we have computationally discovered several new phases in the Li–Ni–B ternary system. The newly discovered LiNiB, Li 2 Ni 3 B, and Li 2 NiB phases expand the existing theoretical database, and the convex-hull surface of Li–Ni–B has been re-constructed. The lowest energy structure of the LiNiB compound has been found by an adaptive genetic algorithm with layered motif, which matches with the experimentally determined structure. According to our electrochemical calculations, LiNiB and another predicted layered Li 2 NiB compounds have great potential as anode materials for lithium batteries. The Li 2 Ni 3 B compound with the space group P4 3 32 was predicted to crystallize in a cubic structure composed of distorted octahedral units of BNi 6 , which is isostructural to two noncentrosymmetric superconductors Li 2 Pd 3 B and Li 2 Pt 3 B. While we were unable to experimentally confirm the Li 2 Ni 3 B compound utilizing the hydride synthetic route, attempts to synthesize this compound by alternate methods remain highly desirable, considering its potential superconducting properties.

36 MATERIALS SCIENCE↗
NASA NTRS2018

UV Capabilities of the CETUS Multi-Object Spectrometer (MOS) and NUV/FUV Camera

The Cosmic Evolution Through UV Spectroscopy (CETUS) concept enables parallel observations by the UV multiobject spectrometer (MOS) and near-UV/far-UV camera which operate simultaneously but independently with their separate field of views. The near-UV MOS can target up to 100 objects at a time without confusion with nearby sources or background zodiacal light. This multiplexing will allow over 100,000 galaxies to be observed over a typical mission lifetime. The MOS includes a next-generation micro-shutter array (NGMSA), an efficient aspheric Offner-like spectrometer design with a convex grating, and nanotube light traps for suppressing unwanted wavelengths. The NUV/FUV Camera has the capability to image in a range of sub-bands from 115-400 nm at the same time the MOS is operating at 180-350 nm. The UV camera has a similar Offner-like relay, selectable filters, and two separate detectors to optimize observing in either the far-UV (115-175 nm) or the near-UV (180-400 nm) utilizing a CsI Micro-Channel Plate detector (MCP) and a CCD respectively.

The Cosmic Evolution Through UV Spectroscopy (CETU↗
DOE OSTI2013

Generating moment matching scenarios using optimization techniques

An optimization based method is proposed to generate moment matching scenarios for numerical integration and its use in stochastic programming. The main advantage of the method is its flexibility: it can generate scenarios matching any prescribed set of moments of the underlying distribution rather than matching all moments up to a certain order, and the distribution can be defined over an arbitrary set. This allows for a reduction in the number of scenarios and allows the scenarios to be better tailored to the problem at hand. The method is based on a semi-infinite linear programming formulation of the problem that is shown to be solvable with polynomial iteration complexity. A practical column generation method is implemented. The column generation subproblems are polynomial optimization problems; however, they need not be solved to optimality. It is found that the columns in the column generation approach can be efficiently generated by random sampling. The number of scenarios generated matches a lower bound of Tchakaloff's. The rate of convergence of the approximation error is established for continuous integrands, and an improved bound is given for smooth integrands. Extensive numerical experiments are presented in which variants of the proposed method are compared to Monte Carlo and quasi-Monte Carlo methods on both numerical integration problems and stochastic optimization problems. The benefits of being able to match any prescribed set of moments, rather than all moments up to a certain order, is also demonstrated using optimization problems with 100-dimensional random vectors. Here, empirical results show that the proposed approach outperforms Monte Carlo and quasi-Monte Carlo based approaches on the tested problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Arbitrage and Capacity Firming in Coordination with Day-Ahead Bidding of a Hybrid PV Plant: Preprint

A hybrid PV plant (HPP) combines a photovoltaic (PV) plant with a battery energy storage system (BESS), which is considered a promising step towards the future of renewable power plants by the U.S. Department of Energy. When the renewable penetration reaches a significant level, a hybrid PV plant can bid in as a controllable thermal plant in the future electricity market. In this study, a bidding and BESS scheduling model is proposed for the HPP. The robust optimization (RO) technique has been utilized to identify the worst-case scenario of uncertainties during the bidding process. To address the overly conservative issue of the single-stage RO, we have decoupled the BESS schedule for arbitrage and PV capacity firming by a two-stage RO formulation. By comparing the output of single-stage RO and two-stage RO, the two-stage RO bids and schedules in a more aggressive manner, which increases the income of HPP. Also, the penalty of under-generation is considered in our model so that the day-ahead bidding decision and arbitrage schedules can be adjusted based on the potential UNDER-GENERATION penalty. Because the proposed model is non-convex and contains multi-stages, the Column-and-Constraint Generation (C&CG) algorithm is applied to the model as the solution. The proposed model has shown better economic performance compared to a state-of-art single-stage bidding method in case studies.

BESS scheduling↗
DOE OSTI2024

Towards optimal sensor placement for inverse problems in spaces of measures

The objective of this work is to quantify the reconstruction error in sparse inverse problems with measures and stochastic noise, motivated by optimal sensor placement. To be useful in this context, the error quantities must be explicit in the sensor configuration and robust with respect to the source, yet relatively easy to compute in practice, compared to a direct evaluation of the error by a large number of samples. In particular, we consider the identification of a measure consisting of an unknown linear combination of point sources from a finite number of measurements contaminated by Gaussian noise. The statistical framework for recovery relies on two main ingredients: first, a convex but non-smooth variational Tikhonov point estimator over the space of Radon measures and, second, a suitable mean-squared error based on its Hellinger–Kantorovich distance to the ground truth. To quantify the error, we employ a non-degenerate source condition as well as careful linearization arguments to derive a computable upper bound. This leads to asymptotically sharp error estimates in expectation that are explicit in the sensor configuration. Thus they can be used to estimate the expected reconstruction error for a given sensor configuration and guide the placement of sensors in sparse inverse problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

An efficient algorithm for solving the generalized trust region subproblem

In this paper, we consider the interval bounded generalized trust region subproblem (GTRS) which is the problem of minimizing a general quadratic function subject to an upper and lower bounded general quadratic constraint. Under the assumption that two matrices from the objective and the constraint functions can be simultaneously diagonalizable via congruence, a diagonalization-based algorithm is introduced to solve it by showing that GTRS is indeed equivalent to a linearly constrained convex univariate problem. Some numerical experiments are given to show the effectiveness of the proposed method and to compare it with the extended Rendl–Wolkowicz algorithm due to Pong and Wolkowicz.

97 MATHEMATICS AND COMPUTING↗
NASA NTRSDate not supplied

Multiple-Effector Control Allocation: Theory and Practice

Redundant controls are ubiquitous in many aerospace domains, including aircraft, spacecraft, and launch vehicles. Multiple control effectors having different capabilities (e.g., reaction controls, aerosurfaces, and vectored engines) must be optimally allocated to achieve high-performance and robust vehicle control, while considering different constraints, cost, or performance metrics associated with various control mixing schemes. These can include force or deflection limits, rate limits, propellant usage or drag penalties, cross-axis coupling, uncertainties, or even servoelastic interactions. This presentation introduces the fundamentals of control allocation theory, based on linear algebra and convex sets, using a handful of examples taken from the air and space vehicle domains. It is shown that even simple methods can provide verifiable and quantifiable performance benefits over ad-hoc approaches, and can support enhanced functions like fault tolerance and control reconfiguration.

Bill Benson↗
DOE OSTI2018

Tightening McCormick Relaxations Toward Global Solution of the ACOPF Problem

Here, we show that a strong upper bound on the objective of the alternating current optimal power flow (ACOPF) problem can significantly improve the effectiveness of optimization-based bounds tightening (OBBT) on a number of relaxations. We additionally compare the performance of relaxations of the ACOPF problem, including the rectangular form without reference bus constraints, the rectangular form with reference bus constraints, and the polar form. We find that relaxations of the rectangular form significantly strengthen existing relaxations if reference bus constraints are included. Overall, relaxations of the polar form perform the best. However, neither the rectangular nor the polar form dominates the other. Ultimately, with these strategies, we are able to reduce the optimality gap to less than 0.1% on all but 5 NESTA test cases with up to 300 buses by performing OBBT alone.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Toward active disruption avoidance via real-time estimation of the safe operating region and disruption proximity in tokamaks

This paper describes a real-time capable algorithm for identifying the safe operating region around a tokamak operating point. The region is defined by a convex set of linear constraints, from which the distance of a point from a disruptive boundary can be calculated. The disruptivity of points is calculated from an empirical machine learning predictor that generates the likelihood of disruption. While the likelihood generated by such empirical models can be compared to a threshold to trigger a disruption mitigation system, the safe operating region calculation enables active optimization of the operating point to maintain a safe margin from disruptive boundaries. The proposed algorithm is tested using a random forest disruption predictor fit on data from DIII-D. The safe operating region identification algorithm is applied to historical data from DIII-D showing the evolution of disruptive boundaries and the potential impact of optimization of the operating point. Real-time relevant execution times are made possible by parallelizing many of the calculation steps and implementing the algorithm on a graphics processing unit. Lastly, a real-time capable algorithm for optimizing the target operating point within the identified constraints is also proposed and simulated.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Optimizing lane reversals in transportation networks to reduce traffic congestion: A global optimization approach

This paper studies how to reduce the overall travel time of commuters in a transportation network by reversing the direction of some lanes in the network using a macroscopic network-wide perspective. Similar to the Network Design Problem, the lane reversal problem has been shown to be NP-hard given the dependence of the users’ route selection on the lane direction decision. Herein, we propose and compare three efficient methods to solve the routing and lane reversal problem jointly. First, we introduce an alternating method that decouples the routing and lane assignment problems. Second, we propose a Frank–Wolfe method that jointly takes gradient steps to adjust both the lane assignment and routing decisions. Third, we propose a convex approximation method that uses a threshold-based approach to convexify the joint routing and lane reversal objective. The convex approximation method is advantageous since it finds a global optimum solution for the approximated problem and it enables the possibility to include linear constraints. Using this method, we extend the main formulation to be able to limit a maximum number of reversed lanes, as well as to incorporate multiple origin–destination (OD) patterns. We test the proposed methods in a case study using the transportation network of Eastern Massachusetts where our results indicate an overall reduction in travel times of 4.7% by selecting the best 15 reversals. Moreover, using a small test network, we investigate the performance of the lane reversal strategies as a function of the OD demand symmetry. As expected, we observe that when the OD demand is very asymmetric (e.g., for a single OD pair, evacuations, large events), the reduction in travel times is larger than the symmetric case, reaching travel time reductions of 60%.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2015

Compressed-sensing-based content-driven hierarchical reconstruction: Theory and application to C-arm cone-beam tomography

Purpose: This paper addresses the reconstruction of x-ray cone-beam computed tomography (CBCT) for interventional C-arm systems. Subsampling of CBCT is a significant issue with C-arms due to their slow rotation and to the low frame rate of their flat panel x-ray detectors. The aim of this work is to propose a novel method able to handle the subsampling artifacts generally observed with analytical reconstruction, through a content-driven hierarchical reconstruction based on compressed sensing. Methods: The central idea is to proceed with a hierarchical method where the most salient features (high intensities or gradients) are reconstructed first to reduce the artifacts these features induce. These artifacts are addressed first because their presence contaminates less salient features. Several hierarchical schemes aiming at streak artifacts reduction are introduced for C-arm CBCT: the empirical orthogonal matching pursuit approach with the ℓ{sub 0} pseudonorm for reconstructing sparse vessels; a convex variant using homotopy with the ℓ{sub 1}-norm constraint of compressed sensing, for reconstructing sparse vessels over a nonsparse background; homotopy with total variation (TV); and a novel empirical extension to nonlinear diffusion (NLD). Such principles are implemented with penalized iterative filtered backprojection algorithms. For soft-tissue imaging, the authors compare the use of TV and NLD filters as sparsity constraints, both optimized with the alternating direction method of multipliers, using a threshold for TV and a nonlinear weighting for NLD. Results: The authors show on simulated data that their approach provides fast convergence to good approximations of the solution of the TV-constrained minimization problem introduced by the compressed sensing theory. Using C-arm CBCT clinical data, the authors show that both TV and NLD can deliver improved image quality by reducing streaks. Conclusions: A flexible compressed-sensing-based algorithmic approach is proposed that is able to accommodate for a wide range of constraints. It is successfully applied to C-arm CBCT images that may not be so well approximated by piecewise constant functions.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2026

RegularizedOptimization.jl: A Julia framework for regularized and nonsmooth optimization

RegularizedOptimization.jl is a Julia package that implements families of quadratic regularization and trust-region methods for solving the nonsmooth optimization problem $^{\textrm{minimize}}_{𝑥∈ℝ^𝑛}$ 𝑓(𝑥) + ℎ(𝑥) subject to 𝑐(𝑥) = 0, (1) where 𝑓 ∶ ℝ 𝑛 → ℝ and 𝑐 ∶ ℝ 𝑛 → ℝ 𝑚 are continuously differentiable, and ℎ ∶ ℝ 𝑛 → ℝ∪{+∞} is lower semi-continuous. The nonsmooth objective ℎ can be a regularizer, such as a sparsity inducing penalty, model simple constraints, such as 𝑥 belonging to a simple convex set, or can be a combination of both. All 𝑓, ℎ, and 𝑐 can be nonconvex. RegularizedOptimization.jl provides a modular and extensible framework for solving (1), and developing novel solvers. Currently, the following solvers are implemented: • Trust-region solvers TR and TRDH (Aravkin et al., 2022; Leconte & Orban, 2025) • Quadratic regularization solvers R2, R2DH and R2N (Aravkin et al., 2022; Diouane, Habiboullah, et al., 2024) • Levenberg-Marquardt solvers LM and LMTR (Aravkin et al., 2024) used when 𝑓 is a least-squares residual. • Augmented Lagrangian solver AL (De Marchi et al., 2023). All solvers rely on first derivatives of 𝑓 and 𝑐, and optionally on their second derivatives in the form of Hessian-vector products. If second derivatives are not available, quasi-Newton approximations can be used. In addition, the proximal mapping of the nonsmooth part ℎ, or adequate models thereof, must be evaluated. At each iteration, a step is computed by solving a subproblem of the form (1) inexactly, in which 𝑓, ℎ, and 𝑐 are replaced with appropriate models around the current iterate. The solvers R2, R2DH, and TRDH are particularly well suited to solve the subproblems, though they are general enough to solve (1). All solvers are allocation-free, so re-solves incur no additional allocations. To illustrate our claim of extensibility, a first version of the AL solver was implemented by an external contributor. Furthermore, a nonsmooth penalty approach, described in Diouane, Gollier, et al. (2024), is currently being developed, that relies on the library to efficiently solve the subproblems.

Gollier, Maxence [Polytechnique Montréal, QC (Cana↗
DOE OSTI2016

Bounding the solutions of parametric weakly coupled second-order semilinear parabolic partial differential equations

Here in this paper, two novel techniques for bounding the solutions of parametric weakly coupled second-order semilinear parabolic partial differential equations are developed. The first provides a theorem to construct interval bounds, while the second provides a theorem to construct lower bounds convex and upper bounds concave in the parameter. The convex/concave bounds can be significantly tighter than the interval bounds because of the wrapping effect suffered by interval analysis in dynamical systems. Both types of bounds are computationally cheap to construct, requiring solving auxiliary systems twice and four times larger than the original system, respectively. An illustrative numerical example of bound construction and use for deterministic global optimization within a simple serial branch-and-bound algorithm, implemented numerically using interval arithmetic and a generalization of McCormick's relaxation technique, is presented. Finally, problems within the important class of reaction-diffusion systems may be optimized with these tools.

42 ENGINEERING↗