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

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Inexact Newton-CG algorithms with complexity guarantees

Abstract We consider variants of a recently developed Newton-CG algorithm for nonconvex problems (Royer, C. W. & Wright, S. J. (2018) Complexity analysis of second-order line-search algorithms for smooth nonconvex optimization. SIAM J. Optim., 28, 1448–1477) in which inexact estimates of the gradient and the Hessian information are used for various steps. Under certain conditions on the inexactness measures, we derive iteration complexity bounds for achieving $\epsilon $-approximate second-order optimality that match best-known lower bounds. Our inexactness condition on the gradient is adaptive, allowing for crude accuracy in regions with large gradients. We describe two variants of our approach, one in which the step size along the computed search direction is chosen adaptively, and another in which the step size is pre-defined. To obtain second-order optimality, our algorithms will make use of a negative curvature direction on some steps. These directions can be obtained, with high probability, using the randomized Lanczos algorithm. In this sense, all of our results hold with high probability over the run of the algorithm. We evaluate the performance of our proposed algorithms empirically on several machine learning models. Our approach is a first attempt to introduce inexact Hessian and/or gradient information into the Newton-CG algorithm of Royer & Wright (2018, Complexity analysis of second-order line-search algorithms for smooth nonconvex optimization. SIAM J. Optim., 28, 1448–1477).

Mathematics↗
NASA NTRS1991

Spectroscopy of an unusual emission line M star

Moderate-resolution spectroscopy of an unusual late-type faint emission-line star, PC 0025 + 0047, is reported. A very strong (greater than 250 A equivalent width) an H-alpha emission line was detected by the present automated line search algorithm. The spectrum was found to have two unresolved emission lines (H-alpha and H-beta) near zero velocity, superposed on the absorption spectrum of a very red M dwarf which has strong K I, and relatively weak bands of TiO. From the weakness of the subordinate lines of Na I (8192 A) and other spectral features, it is inferred that it is definitely a cooler, and probably fainter, analog of LHS 2924. The strength of the emission lines indicates that PC 0025 + 0447 is very young and may be a fading predecessor brown drawf at an estimated M(bol) approaching 14m at a distance of about 60 pc.

Schneider, Donald P.↗
NASA NTRS2011

Enhanced Fuel-Optimal Trajectory-Generation Algorithm for Planetary Pinpoint Landing

An enhanced algorithm is developed that builds on a previous innovation of fuel-optimal powered-descent guidance (PDG) for planetary pinpoint landing. The PDG problem is to compute constrained, fuel-optimal trajectories to land a craft at a prescribed target on a planetary surface, starting from a parachute cut-off point and using a throttleable descent engine. The previous innovation showed the minimal-fuel PDG problem can be posed as a convex optimization problem, in particular, as a Second-Order Cone Program, which can be solved to global optimality with deterministic convergence properties, and hence is a candidate for onboard implementation. To increase the speed and robustness of this convex PDG algorithm for possible onboard implementation, the following enhancements are incorporated: 1) Fast detection of infeasibility (i.e., control authority is not sufficient for soft-landing) for subsequent fault response. 2) The use of a piecewise-linear control parameterization, providing smooth solution trajectories and increasing computational efficiency. 3) An enhanced line-search algorithm for optimal time-of-flight, providing quicker convergence and bounding the number of path-planning iterations needed. 4) An additional constraint that analytically guarantees inter-sample satisfaction of glide-slope and non-sub-surface flight constraints, allowing larger discretizations and, hence, faster optimization. 5) Explicit incorporation of Mars rotation rate into the trajectory computation for improved targeting accuracy. These enhancements allow faster convergence to the fuel-optimal solution and, more importantly, remove the need for a "human-in-the-loop," as constraints will be satisfied over the entire path-planning interval independent of step-size (as opposed to just at the discrete time points) and infeasible initial conditions are immediately detected. Finally, while the PDG stage is typically only a few minutes, ignoring the rotation rate of Mars can introduce 10s of meters of error. By incorporating it, the enhanced PDG algorithm becomes capable of pinpoint targeting.

Acikmese, Behcet↗
DOE OSTI2025

Analysis of the SiMPL Method for Density-Based Topology Optimization

We present a rigorous convergence analysis of a new method for density-based topology optimization that provides pointwise bound-preserving design updates and faster convergence than other popular first-order topology optimization methods. Due to its strong bound preservation, the method is exceptionally robust, as demonstrated in numerous examples here and in the companion article [D. Kim et al., Struct. Multidiscip. Optim., 68 (2025), 74]. Furthermore, it is easy to implement with clear structure and analytical expressions for the updates. Our analysis covers two versions of the method, characterized by the employed line search strategies. We consider a modified Armijo backtracking line search and a Bregman backtracking line search. For both line search algorithms, our algorithm delivers a strict monotone decrease in the objective function and further intuitive convergence properties, e.g., strong and pointwise convergence of the density variables on the active sets, norm convergence to zero of the increments, convergence of the Lagrange multipliers, and more. In addition, the numerical experiments demonstrate apparent mesh-independent convergence of the algorithm. Here, we refer to the new algorithm as the SiMPL method (pronounced “simple”), which stands for Sigmoidal Mirror descent with a Projected Latent variable.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Compact representations of structured BFGS matrices

For general large-scale optimization problems compact representations exist in which recursive quasi-Newton update formulas are represented as compact matrix factorizations. For problems in which the objective function contains additional structure, recent structured quasi-Newton methods exploit available second-derivative information and approximate unavailable second derivatives. Here, this article develops the compact representations of two structured Broyden-Fletcher-Goldfarb-Shanno update formulas. The compact representations enable efficient limited memory and initialization strategies. Two limited memory line search algorithms are described for which extensive numerical results demonstrate the efficacy of the algorithms, including comparisons to IPOPT on large machine learning problems, and to L-BFGS on a real world large scale ptychographic imaging application.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A simple introduction to the SiMPL method for density-based topology optimization

We introduce a novel method for solving density-based topology optimization problems: Sigmoidal Mirror descent with a Projected Latent variable (SiMPL). The SiMPL method (pronounced as “the simple method”) optimizes a design using only first-order derivative information of the objective function. The bound constraints on the density field are enforced with the help of the (negative) Fermi–Dirac entropy, which is also used to define a non-symmetric distance function called a Bregman divergence on the set of admissible designs. This Bregman divergence leads to a simple update rule that is further simplified with the help of a so-called latent variable. Because the SiMPL method involves discretizing the latent variable, it produces a sequence of pointwise-feasible iterates, even when high-order finite elements are used in the discretization. Numerical experiments demonstrate that the method outperforms other popular first-order optimization algorithms. In conclusion, to outline the general applicability of the technique, we include examples with (self-load) compliance minimization and compliant mechanism optimization problems.

Calculus of Variations and Optimization↗
DOE OSTI2020

Geometry-independent microstructure optimization for electron beam powder bed fusion additive manufacturing

The ability to manipulate the formation of microstructure is one of the potential advantages of additive manufacturing. Yet, the additive manufacturing process is riddled with complex interactions between processing parameters, geometry, and spot melting sequence which makes the task of controlling microstructure challenging. This paper proposes a method to solve the microstructure texture optimization problem by leveraging established optimization techniques and increasingly fast and accurate analytical heat transfer models. Respectively, we apply two different optimization algorithms, genetic algorithm and concurrent greedy line search, in order to induce arbitrarily shaped microstructure regions and we use a heat transfer model to evaluate the fitness of solutions in an iterative approach that is far more efficient than pure trial and error. The objective of the optimization algorithm is to control local thermal conditions – hence microstructure formation – during the melting process by manipulating the order and the dwell time of all the points of the infill pattern sequence. We then analyze the optimized sequence to determine important path characteristics that affect the microstructure formation. Through examples, we show that relative order and frequency, as measured by weighted average and variance of spot order, are important factors that influence the final characteristics.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Pseudospectral convex optimization for on-ramp merging control of connected vehicles

It can be a daunting task for human drivers to merge into highways because of the intricate vehicle negotiations and potential risk within limited time and space. Connected vehicle (CV) technologies could be a solution to this problem and offer many benefits to the road safety, traffic mobility, and energy efficiency. However, real-time optimal control of CVs is still an open challenge, due to the nonlinear vehicle dynamics, non-convex fuel consumption model, and highly dynamic uncertain inter-vehicle interactions. To tackle these issues, a novel real-time optimal control approach that balances the computational efficiency and solution optimality is proposed for the purpose of onboard application. To this end, the pseudospectral collocation method is integrated with a sequential convex programming approach to develop two new optimization algorithms, which are implemented within a model predictive control (MPC) framework to allow for real-time generation of optimal merging speed profiles. One algorithm leverages the line search technique to improve convergence, and the other benefits from the trust region method for better computational efficiency. The optimality and convergence process of both proposed algorithms are investigated by comparing their solutions with a popular non-linear solver. Furthermore, simulation results show that the proposed methods outperform the benchmark in terms of computational cost, fuel consumption, and traffic efficiency. In particular, the proposed fuel-economy merging rule can save 57.1% fuel consumption on average on four different traffic volumes. Meanwhile, the proposed optimal control algorithms can reduce 2.2% travel time on average comparing to the “first-in-first-out” merging rule.

33 ADVANCED PROPULSION SYSTEMS↗
NASA NTRS1992

Automated detection of jet contrails using the AVHRR split window

This paper investigates the automated detection of jet contrails using data from the Advanced Very High Resolution Radiometer. A preliminary algorithm subtracts the 11.8-micron image from the 10.8-micron image, creating a difference image on which contrails are enhanced. Then a three-stage algorithm searches the difference image for the nearly-straight line segments which characterize contrails. First, the algorithm searches for elevated, linear patterns called 'ridges'. Second, it applies a Hough transform to the detected ridges to locate nearly-straight lines. Third, the algorithm determines which of the nearly-straight lines are likely to be contrails. The paper applies this technique to several test scenes.

Engelstad, M.↗
NASA NTRS2017

Low-Thrust Trajectory Optimization with Simplified SQP Algorithm

The problem of low-thrust trajectory optimization in highly perturbed dynamics is a stressing case for many optimization tools. Highly nonlinear dynamics and continuous thrust are each, separately, non-trivial problems in the field of optimal control, and when combined, the problem is even more difficult. This paper de-scribes a fast, robust method to design a trajectory in the CRTBP (circular restricted three body problem), beginning with no or very little knowledge of the system. The approach is inspired by the SQP (sequential quadratic programming) algorithm, in which a general nonlinear programming problem is solved via a sequence of quadratic problems. A few key simplifications make the algorithm presented fast and robust to initial guess: a quadratic cost function, neglecting the line search step when the solution is known to be far away, judicious use of end-point constraints, and mesh refinement on multiple shooting with fixed-step integration.In comparison to the traditional approach of plugging the problem into a “black-box” NLP solver, the methods shown converge even when given no knowledge of the solution at all. It was found that the only piece of information that the user needs to provide is a rough guess for the time of flight, as the transfer time guess will dictate which set of local solutions the algorithm could converge on. This robustness to initial guess is a compelling feature, as three-body orbit transfers are challenging to design with intuition alone. Of course, if a high-quality initial guess is available, the methods shown are still valid.We have shown that endpoints can be efficiently constrained to lie on 3-body repeating orbits, and that time of flight can be optimized as well. When optimizing the endpoints, we must make a trade between converging quickly on sub-optimal endpoints or converging more slowly on end-points that are arbitrarily close to optimal. It is easy for the mission design engineer to adjust this trade based on the problem at hand.The biggest limitation to the algorithm at this point is that multi-revolution transfers (greater than 2 revolutions) do not work nearly as well. This restriction comes in because the relationship between node 1 and node N becomes increasingly nonlinear as the angular distance grows. Trans-fers with more than about 1.5 complete revolutions generally require the line search to improve convergence. Future work includes: Comparison of this algorithm with other established tools; improvements to how multiple-revolution transfers are handled; parallelization of the Jacobian computation; in-creased efficiency for the line search; and optimization of many more trajectories between a variety of 3-body orbits.

Parrish, Nathan L.↗
NASA NTRS1994

Spectroscopic CCD surveys for quasars at large redshift. 3: The Palomar Transit Grism Survey catalog

This paper reports the initial results of the Palomar Transit Grism Survey (PTGS). The PTGS was designed to produce a sample of z greater than 2.7 quasars that were identified by well-defined selection criteria. The survey consists of six narrow (approximately equal to 8.5 min wide) strips of sky; the total effective area is 61.47 sq deg. Low-resolution slitless spectra, covering the wavelength range from 4400 to 7500 A, were obtained for approximately 600 000 objects. The wavelength- and flux-calibrated spectra were searched for emission lines with an automatic software algorithm. A total to 1655 emission features in the grism data satisfied our signal-to-noise ratio and equivalent width selection criteria; subsequent slit spectroscopy of the candidates confirmed the existence of 1052 lines (928 different objects). Six groups of emission lines were detected in the survey: Lyman alpha + N V, C IV, C III1, Mg II, H Beta + (O III), and H alpha + (S II). More than two-thirds of the candidates are low-redshift (z less than 0.45) emission-line galaxies; ninety objects are high-redshift quasars (z greater than 2.7) detected via their Lyman alpha + N V emission lines. The survey contains three previously unknown quasars brighter than 17th magnitude; all three have redshifts of approximately equal to 1.3. In this paper we present the observational properties of the survey, the algorithms used to select the emission-line candidates, and the catalog of emission-line objects.

Schneider, Donald P.↗
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 OSTI2023

Accelerated Sparse Recovery via Gradient Descent with Nonlinear Conjugate Gradient Momentum

This paper applies an idea of adaptive momentum for the nonlinear conjugate gradient to accelerate optimization problems in sparse recovery. Specifically, we consider two types of minimization problems: a (single) differentiable function and the sum of a non-smooth function and a differentiable function. In the first case, we adopt a fixed step size to avoid the traditional line search and establish the convergence analysis of the proposed algorithm for a quadratic problem. This acceleration is further incorporated with an operator splitting technique to deal with the non-smooth function in the second case. As a result, we use the convex ι 1 and the nonconvex ι 1 – ι 2 functionals as two case studies to demonstrate the efficiency of the proposed approaches over traditional methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A unified funnel restoration SQP algorithm

We consider nonlinearly constrained optimization problems and discuss a generic double-loop framework consisting of basic algorithmic ingredients that unifies a broad range of nonlinear optimization solvers. This framework has been implemented in the open-source solver Uno, a Swiss Army knife-like C++ optimization framework that unifies many nonlinearly constrained nonconvex optimization solvers. We illustrate the framework with a sequential quadratic programming (SQP) algorithm that maintains an acceptable upper bound on the constraint violation, called a funnel, that is monotonically decreased to control the feasibility of the iterates. Infeasible quadratic subproblems are handled by a feasibility restoration strategy. Globalization is controlled by a line search or a trust-region method. We prove global convergence of the trust-region funnel SQP method, building on known results from filter methods. We implement the algorithm in Uno, and we provide extensive test results for the trust-region line-search funnel SQP on small CUTEst instances.

Kiessling, David [Katholieke Univ. Leuven, Heverle↗
NASA NTRS2011

SAD5 Stereo Correlation Line-Striping in an FPGA

High precision SAD5 stereo computations can be performed in an FPGA (field-programmable gate array) at much higher speeds than possible in a conventional CPU (central processing unit), but this uses large amounts of FPGA resources that scale with image size. Of the two key resources in an FPGA, Slices and BRAM (block RAM), Slices scale linearly in the new algorithm with image size, and BRAM scales quadratically with image size. An approach was developed to trade latency for BRAM by sub-windowing the image vertically into overlapping strips and stitching the outputs together to create a single continuous disparity output. In stereo, the general rule of thumb is that the disparity search range must be 1/10 the image size. In the new algorithm, BRAM usage scales linearly with disparity search range and scales again linearly with line width. So a doubling of image size, say from 640 to 1,280, would in the previous design be an effective 4 of BRAM usage: 2 for line width, 2 again for disparity search range. The minimum strip size is twice the search range, and will produce an output strip width equal to the disparity search range. So assuming a disparity search range of 1/10 image width, 10 sequential runs of the minimum strip size would produce a full output image. This approach allowed the innovators to fit 1280 960 wide SAD5 stereo disparity in less than 80 BRAM, 52k Slices on a Virtex 5LX330T, 25% and 24% of resources, respectively. Using a 100-MHz clock, this build would perform stereo at 39 Hz. Of particular interest to JPL is that there is a flight qualified version of the Virtex 5: this could produce stereo results even for very large image sizes at 3 orders of magnitude faster than could be computed on the PowerPC 750 flight computer. The work covered in the report allows the stereo algorithm to run on much larger images than before, and using much less BRAM. This opens up choices for a smaller flight FPGA (which saves power and space), or for other algorithms in addition to SAD5 to be run on the same FPGA.

Villalpando, Carlos Y.↗
DOE OSTI2024

Force-Free Identification of Minimum-Energy Pathways and Transition States for Stochastic Electronic Structure Theories

Here, the accurate mapping of potential energy surfaces (PESs) is crucial to our understanding of the numerous physical and chemical processes mediated by atomic rearrangements, such as conformational changes and chemical reactions, and the thermodynamic and kinetic feasibility of these processes. Stochastic electronic structure theories, e.g., Quantum Monte Carlo (QMC) methods, enable highly accurate total energy calculations that in principle can be used to construct the PES. However, their stochastic nature poses a challenge to the computation and use of forces and Hessians, which are typically required in algorithms for minimum-energy pathway (MEP) and transition state (TS) identification, such as the nudged elastic band (NEB) algorithm and its climbing image formulation. Here, we present strategies that utilize the surrogate Hessian line-search method, previously developed for QMC structural optimization, to efficiently identify MEP and TS structures without requiring force calculations at the level of the stochastic electronic structure theory. By modifying the surrogate Hessian algorithm to operate in path-orthogonal subspaces and at saddle points, we show that it is possible to identify MEPs and TSs by using a force-free QMC approach. We demonstrate these strategies via two examples, the inversion of the ammonia (NH 3 ) molecule and the nucleophilic substitution (S N 2) reaction F – + CH 3 F → FCH 3 + F – . We validate our results using Density Functional Theory (DFT)- and Coupled Cluster (CCSD, CCSD(T))-based NEB calculations. We then introduce a hybrid DFT-QMC approach to compute thermodynamic and kinetic quantities, free energy differences, rate constants, and equilibrium constants that incorporates stochastically optimized structures and their energies, and show that this scheme improves upon DFT accuracy. Our methods generalize straightforwardly to other systems and other high-accuracy theories that similarly face challenges computing energy gradients, paving the way for highly accurate PES mapping, transition state determination, and thermodynamic and kinetic calculations at significantly reduced computational expense.

Iyer, Gopal R.↗
NASA NTRS1999

Remote Sensing of Rain

The first problem addressed concerns passive-microwave rain retrievals. Most current approaches start by building off-line a cloud-model-derived database. Given data, the retrieval algorithms search the database for the microwave temperatures "closest" to the observed data, then after some fine-tuning (performed in different ways by different implementations) the rain is estimated to be that which corresponds to the selected (and fine-tuned) set of database temperatures. These approaches have three drawbacks: they cannot properly take into account the ambiguities which arise from the fact that several rain scenarios can produce the same observed temperatures; they are quite inefficient since they require manipulating a large database along with often complex "fine-tuning" procedures; and they cannot refine their estimates if additional data is available. This past year we have derived closed formulae relating observed microwave brightness temperatures, T(sub b), and the underlying rain rates, R: average T(sub b) =f (rain) and average rain = g (T(sub b)), along with the corresponding covariance matrices. These results are sufficient to describe the conditional probabilities p(R/T(sub b)) and p(T(sub b)/R) to second order. Progress has also been made towards deriving a robust description of the rain drop size distribution (DSD). The widespread approach consisting in parameterizing the DSD as a gamma-distribution in terms of the drop diameter D suffers from the facts that, in reality, the DSD is not a smooth function of D and that the largely arbitrary Gamma model imposes unintended behavior, which has implications on any quantities derived from the DSD model. We have therefore developed a non-parametric yet practical description of the DSD, which is particularly well-suited for use in remote-sensing applications. The diagram on the left shows a comparison between an actual DSD sample and the truncated non-parametric representation. One figure shows the relation between radar reflectivity and rain rate derived using this representation. Validation of the Tropical Rainfall Measuring Mission (TRMM) radar-radiometer combined R and DSD algorithm is underway. This algorithm was designed to make optimal use of the instantaneous reflectivity profiles measured by the TRMM radar and the microwave brightness temperatures measured by the TRMM passive radiometer. So far, it appears to be the most reliable TRMM rain algorithm.

Haddad, Ziad S.↗
DOE OSTI2020

Efficient optimization method for finding minimum energy paths of magnetic transitions

Here, efficient algorithms for the calculation of minimum energy paths of magnetic transitions are implemented within the geodesic nudged elastic band (GNEB) approach. While an objective function is not available for GNEB and a traditional line search can, therefore, not be performed, the use of limited memory Broyden–Fletcher–Goldfarb–Shanno (LBFGS) and conjugate gradient algorithms in conjunction with orthogonal spin optimization (OSO) approach is shown to greatly outperform the previously used velocity projection and dissipative Landau–Lifschitz dynamics optimization methods. The implementation makes use of energy weighted springs for the distribution of the discretization points along the path and this is found to improve performance significantly. The various methods are applied to several test problems using a Heisenberg-type Hamiltonian, extended in some cases to include Dzyaloshinskii–Moriya and exchange interactions beyond nearest neighbours. Minimum energy paths are found for magnetization reversals in a nano-island, collapse of skyrmions in two-dimensional layers and annihilation of a chiral bobber near the surface of a three-dimensional magnet. The LBFGS-OSO method is found to outperform the dynamics based approaches by up to a factor of 8 in some cases.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗