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NASA NTRS2020

Texas Spectroscopic Search for Lyα Emission at the End of Reionization. III. The Lyα Equivalent-width Distribution and Ionized Structures at z > 7

Lyα emission from galaxies can be utilized to characterize the ionization state in the intergalactic medium (IGM). We report our search for Lyα emission at z > 7 using a comprehensive Keck/MOSFIRE near-infrared spectroscopic data set, as part of the Texas Spectroscopic Search for Lyα Emission at the End of Reionization Survey. We analyze data from 10 nights of MOSFIRE observations which together target 72 high-z candidate galaxies in the GOODS-N field, all with deep exposure times of 4.5–19 hr. Utilizing an improved automated emission-line search, we report 10 Lyα emission lines detected (>4σ) at z > 7, significantly increasing the spectroscopically confirmed sample. Our sample includes large equivalent-width (EW) Lyα emitters (>50 Å), and additional tentative Lyα emission lines detected at 3σ–4σ from five additional galaxies. We constrain the Lyα EW distribution at z ~ 7.6, finding a significant drop from z ≲ 6, suggesting an increasing fraction of neutral hydrogen (H I) in the IGM in this epoch. We estimate the Lyα transmission through the IGM (=EW(z)~7.6/EW(z~2–6)) and infer an IGM H I fraction (X(HI)) of 49 (+19,-19)% at z ~ 7.6, which is lower in modest tension (>1σ) with recent measurements at z ~ 7.6. The spatial distribution of the detected Lyα emitters implies the presence of a potential highly ionized region at z ~ 7.55, which hosts four Lyα emitters within a ∼40 cMpc spatial separation. The prominence of this ionized region in our data set could explain our lower inferred value of X(HI), though our analysis is also sensitive to the chosen reference Lyα EW distribution values and reionization models.

Intae Jung↗

NASA NTRS1983

Engineering calculations for communications satellite systems planning

Progress is reported on a computer code to improve the efficiency of spectrum and orbit utilization for the Broadcasting Satellite Service in the 12 GHz band for Region 2. It implements a constrained gradient search procedure using an exponential objective function based on aggregate signal to noise ratio and an extended line search in the gradient direction. The procedure is tested against a manually generated initial scenario and appears to work satisfactorily. In this test it was assumed that alternate channels use orthogonal polarizations at any one satellite location.

Martin, C. H.↗

NASA NTRS2004

SIS Mixer Design for a Broadband Millimeter Spectrometer Suitable for Rapid Line Surveys and Redshift Determinations

We present some detail of the waveguide probe and SIS mixer chip designs for a low-noise 180-300 GHz double- sideband receiver with an instantaneous RF bandwidth of 24 GHz. The receiver's single SIS junction is excited by a broadband, fixed-tuned waveguide probe on a silicon substrate. The IF output is coupled to a 6-18 GHz MMIC low- noise preamplifier. Following further amplification, the output is processed by an array of 4 GHz, 128-channel analog autocorrelation spectrometers (WASP 11). The single-sideband receiver noise temperature goal of 70 Kelvin will provide a prototype instrument capable of rapid line surveys and of relatively efficient carbon monoxide (CO) emission line searches of distant, dusty galaxies. The latter application's goal is to determine redshifts by measuring the frequencies of CO line emissions from the star-forming regions dominating the submillimeter brightness of these galaxies. Construction of the receiver has begun; lab testing should begin in the fall. Demonstration of the receiver on the Caltech Submillimeter Observatory (CSO) telescope should begin in spring 2003.

Rice, F.↗

DOE OSTI2022

An indirect approach to optimize the reaction rates of thermal NO formation for diesel engines

With stringent emission regulations, it has become more important for modern diesel engine manufacturers to accurately predict engine-out nitrogen oxide (NO x ) emissions across a wide range of operating conditions. Thermal NO is the major source of engine-out NO x in modern diesel engines. For thermal NO formation, several earlier studies have recommended the forward and reverse reaction rate coefficients of the rate-limiting reaction (O + N 2 ⇌ NO + N). However, due to deficiencies in sub-models and inadequacies of reduced chemical mechanisms to represent diesel combustion, these recommended values more often than not need to be adjusted in reduced order combustion models to accurately predict engine-out NO x . Hence, in this work a systematic and computationally efficient approach has been proposed to streamline the process of determining the optimum reaction rate coefficients. Here, to develop the optimization approach, four different production diesel engines with different operating conditions in terms of speed, load, and exhaust-gas recirculation have been considered. Numerical simulations have been performed using a detailed zero-dimensional velocity-composition-frequency transported probability density function (0D-VCF-tPDF) model that uses hundreds of notional particles to capture in-cylinder stratification. Four different combinations of hydrocarbon and NO x chemical mechanisms were used to represent chemistry. It was found that for the rate-limiting reaction, the pre-exponent factors (A f1 , A r1 ) and activation energies (E A,f1 , E A,r1 ) of the forward and reverse reaction rates follow a linear band in A f1 - E A,f1 and A r1 - E A,r1 space where predicted engine-out NO x match the measured values closely. By encompassing such bands from different engines and considering constraints on activation energies, a reduced search domain of pre-exponent factors and activation energies was constructed that is expected to be applicable to any diesel engine. Eventually, computationally efficient three-line and one-line search approaches were proposed to determine the optimum values of the pre-exponent factors and activation energies that led to a minimum error between measured and predicted engine-out NO x . Finally, these three-line and one-line NO x optimization approaches were applied to a fifth production diesel engine for which the 0D-VCF-tPDF model showed a very good predictive performance in terms of predicting peak pressure, 50% burn rate, and engine-out NO x when compared to measured and 3D-CFD values.

33 ADVANCED PROPULSION SYSTEMS↗

NASA NTRS2020

NuSTAR Observation of GROJ1744−28 at Low Mass Accretion Rate

Context.Neutron stars in low-mass X-ray binaries (LMXBs) are important systems to study the physics of accretion onto compact ob-jects. The system GRO J1744−28 is particularly interesting, as it usually shows clear pulsations as well as X-ray bursts. Additionally,there are claims for a magnetic field of 5×1011G through the detection of a Cyclotron Resonant Scattering Feature (CRSF).Aims.We present the spectral analysis of GRO J1744−28 using∼29 ks of NuSTAR data taken in 2017 February at a low luminosityof 3.2×1036erg s−1(3–50 keV). Our goal is to study the variability of the source spectrum with pulse phase and to search for the claimed CRSF. Methods.The continuum spectrum is modeled with an absorbed power-law with exponential cut-off, and an additional iron line component. We find no obvious indications for a CRSF and therefore perform a detailed cyclotron line search using statistical methods.We perform this search on pulse phase-averaged as well as phase-resolved spectra. Results.GRO J1744−28 was observed at one of the lowest luminosities studied so far. The previously detected Type II X-ray bursts re absent. Clear pulsations at a period of 2.141124(9) Hz are detected. The pulse profile shows an indication of a secondary peak,which was not seen at higher flux. The 4σupper limit for the strength of a CRSF in the 3–20 keV band is 0.07 keV, lower than the strength of the line found at higher luminosity. Conclusions.The detection of pulsations shows that the source did not enter the “propeller” regime, even though the source flux of4.15×10−10erg cm−2s−1was almost one order of magnitude below the threshold for the propeller regime claimed in previous studies on this source. The transition into the propeller regime in GRO J1744−28 must therefore be below a luminosity of 3.2×1036erg s−1(3–50 keV), which implies a surface magnetic field.2.9×1011G and mass accretion rate.1.7×1016g s−1. A change of the CRSF depth as function of luminosity is not unexpected and has been observed in other sources. This result possibly implies a change in emission geometry as function of mass accretion rate to reduce the depth of the line below our detection limit.

Ole König↗

DOE OSTI2022

CLASS: Coronal Line Activity Spectroscopic Survey

We conduct the first systematic survey of a comprehensive set of the twenty optical coronal lines in the spectra of nearly 1 million galaxies observed by the Sloan Digital Sky Survey (SDSS) Data Release 8 catalog. This includes often overlooked high ionization potential lines such as [Ar x] λ5533, [S XII ] λ7609, [Fe XI ] λ7892, and [Fe XIV ] λ5303. We find that, given the limited sensitivity of SDSS, strong coronal line emission is extremely rare, with only ~0.03% of the sample showing at least one coronal line, significantly lower than the fraction of galaxies showing optical narrow line ratios (~17%) or mid-infrared colors (~2%) indicative of nuclear activity. The coronal line luminosities exhibit a large dynamic range, with values ranging from ~10 34 to 10 42 erg s –1 . We find that a vast majority (~80%) of coronal line emitters in dwarf galaxies (M $\star$ < 9.6 × 10 9 M ⊙ ) do not display optical narrow line ratios indicative of nuclear activity, in contrast to higher mass galaxies (~17%). Moreover, we find that the highest ionization potential lines are preferentially found in lower mass galaxies. These findings are consistent with the theory that lower mass black holes found in lower mass galaxies produce a hotter accretion disk, which in turn enhances the higher ionization coronal line spectrum. Future coronal line searches with 30 m class telescopes or JWST may provide a pathway into uncovering the intermediate mass black hole population.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

An adaptive stochastic sequential quadratic programming with differentiable exact augmented lagrangians

In this study, we consider solving nonlinear optimization problems with a stochastic objective and deterministic equality constraints. We assume for the objective that its evaluation, gradient, and Hessian are inaccessible, while one can compute their stochastic estimates by, for example, subsampling. We propose a stochastic algorithm based on sequential quadratic programming (SQP) that uses a differentiable exact augmented Lagrangian as the merit function. To motivate our algorithm design, we first revisit and simplify an old SQP method Lucidi developed for solving deterministic problems, which serves as the skeleton of our stochastic algorithm. Based on the simplified deterministic algorithm, we then propose a non-adaptive SQP for dealing with stochastic objective, where the gradient and Hessian are replaced by stochastic estimates but the stepsizes are deterministic and prespecified. Finally, we incorporate a recent stochastic line search procedure Paquette and Scheinberg into the non-adaptive stochastic SQP to adaptively select the random stepsizes, which leads to an adaptive stochastic SQP. The global "almost sure" convergence for both non-adaptive and adaptive SQP methods is established. Numerical experiments on nonlinear problems in CUTEst test set demonstrate the superiority of the adaptive algorithm.

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 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

Optimizing the optimizer for physics-informed neural networks and Kolmogorov-Arnold networks

Physics-Informed Neural Networks (PINNs) have revolutionized the computation of PDE solutions by integrating partial differential equations (PDEs) into the neural network’s training process as soft constraints, becoming an important component of the scientific machine learning (SciML) ecosystem. More recently, physics-informed Kolmogorv-Arnold networks (PIKANs) have also shown to be effective and comparable in accuracy with PINNs. In their current implementation, both PINNs and PIKANs are mainly optimized using first-order methods like Adam, as well as quasi-Newton methods such as BFGS and its low-memory variant, L-BFGS. However, these optimizers often struggle with highly nonlinear and non-convex loss landscapes, leading to challenges such as slow convergence, local minima entrapment, and (non)degenerate saddle points. In this study, we investigate the performance of Self- Scaled BFGS (SSBFGS), Self-Scaled Broyden (SSBroyden) methods and other advanced quasi-Newton schemes, including BFGS and L-BFGS with different line search strategies. These methods dynamically rescale updates based on historical gradient information, thus enhancing training efficiency and accuracy. We systematically compare these optimizers – using both PINNs and PIKANs – on key challenging PDEs, including the Burgers, Allen-Cahn, Kuramoto-Sivashinsky, Ginzburg-Landau, and Stokes equations. Additionally, we evaluate the performance of SSBFGS and SSBroyden for Deep Operator Network (DeepONet) architectures, demonstrating their effectiveness for data-driven operator learning. Our findings provide state-of-the-art results with orders-of-magnitude accuracy improvements without the use of adaptive weights or any other enhancements typically employed in PINNs. More broadly, our work reveal insights into the effectiveness of quasi-Newton optimization strategies in significantly improving the convergence and accurate generalization of PINNs and PIKANs.

97 MATHEMATICS AND COMPUTING↗

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↗

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.↗

DOE OSTI2023

A Quantum Monte Carlo Study of the Structural, Energetic, and Magnetic Properties of Two-Dimensional H and T Phase VSe 2

Previous works have controversially claimed near-room-temperature ferromagnetism in two-dimensional (2D) VSe 2 , with conflicting results throughout the literature. These discrepancies in magnetic properties between both phases (T and H) of 2D VSe 2 are most likely due to the structural parameters being coupled to the magnetic properties. Specifically, both phases have a close lattice match and similar total energies, which makes it difficult to determine which phase is being observed experimentally. Here, in this study, we used a combination of density functional theory, highly accurate diffusion Monte Carlo (DMC), and a surrogate Hessian line-search optimization technique to resolve the previously reported discrepancy in structural parameters and relative phase stability. With DMC accuracy, we determined the free-standing geometry of both phases and constructed a phase diagram. Our findings demonstrate the successes of the DMC method coupled with the surrogate Hessian structural optimization technique when applied to a 2D magnetic system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

O Corona, where art thou? eROSITA’s view of UV-optical-IR variability-selected massive black holes in low-mass galaxies

Finding massive black holes (MBHs,M BH ≈ 10 4 –10 7 M ⊙ ) in the nuclei of low-mass galaxies $\left( {{M_*}\mathop {\mathop < \limits_ }\limits_ {{10}^{10}}{M_ \odot }} \right)$ is crucial to constrain seeding and growth of black holes over cosmic time, but it is particularly challenging due to their low accretion luminosities. Variability selection via long-term photometric ultraviolet, optical, or infrared (UVOIR) light curves has proved effective and identifies lower-Eddington ratios compared to broad and narrow optical spectral lines searches. In the inefficient accretion regime, X-ray and radio searches are effective, but they have been limited to small samples. Therefore, differences between selection techniques have remained uncertain. Here, we present the first large systematic investigation of the X-ray properties of a sample of known MBH candidates in dwarf galaxies. We extracted X-ray photometry and spectra of a sample of ~200 UVOIR variability-selected MBHs and significantly detected 17 of them in the deepest available SRG/eROSITA image, of which four are newly discovered X-ray sources and two are new secure MBHs. This implies that tens to hundreds of LSST MBHs will have SRG/eROSITA counterparts, depending on the seeding model adopted. Surprisingly, the stacked X-ray images of the many non-detected MBHs are incompatible with standard disk-corona relations, typical of active galactic nuclei, inferred from both the optical and radio fluxes. They are instead compatible with the X-ray emission predicted for normal galaxies. After careful consideration of potential biases, we identified that this X-ray weakness needs a physical origin. A possibility is that a canonical X-ray corona might be lacking in the majority of this population of UVOIR-variability selected low-mass galaxies or that unusual accretion modes and spectral energy distributions are in place for MBHs in dwarf galaxies. This result reveals the potential for severe biases in occupation fractions derived from data from only one waveband combined with SEDs and scaling relations of more massive black holes and galaxies.

Astronomy & Astrophysics↗

DOE OSTI2022

A combined first principles study of the structural, magnetic, and phonon properties of monolayer CrI3

The first magnetic 2D material discovered, monolayer (ML) CrI3, is particularly fascinating due to its ground state ferromagnetism. However, because ML materials are difficult to probe experimentally, much remains unresolved about ML CrI3’s structural, electronic, and magnetic properties. Here, we leverage Density Functional Theory (DFT) and high-accuracy Diffusion Monte Carlo (DMC) simulations to predict lattice parameters, magnetic moments, and spin–phonon and spin–lattice coupling of ML CrI3. We exploit a recently developed surrogate Hessian DMC line search technique to determine CrI3’s ML geometry with DMC accuracy, yielding lattice parameters in good agreement with recently published STM measurements—an accomplishment given the ~10% variability in previous DFT-derived estimates depending upon the functional. Strikingly, we find that previous DFT predictions of ML CrI3’s magnetic spin moments are correct on average across a unit cell but miss critical local spatial fluctuations in the spin density revealed by more accurate DMC. DMC predicts that magnetic moments in ML CrI3 are 3.62 μB per chromium and -0.145 μB per iodine, both larger than previous DFT predictions. The large disparate moments together with the large spin–orbit coupling of CrI3’s I-p orbital suggest a ligand superexchange-dominated magnetic anisotropy in ML CrI3, corroborating recent observations of magnons in its 2D limit. We also find that ML CrI3 exhibits a substantial spin–phonon coupling of ~3.32 cm-1. Our work, thus, establishes many of ML CrI3’s key properties, while also continuing to demonstrate the pivotal role that DMC can assume in the study of magnetic and other 2D materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

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↗

DOE OSTI2021

Optimized structure and electronic band gap of monolayer GeSe from quantum Monte Carlo methods

Here, we have used highly accurate quantum Monte Carlo methods to determine the chemical structure and electronic band gaps of monolayer GeSe. Two-dimensional (2D) monolayer GeSe has received a great deal of attention due to its unique thermoelectric, electronic, and optoelectronic properties with a wide range of potential applications. Density functional theory (DFT) methods have usually been applied to obtain optical and structural properties of bulk and 2D GeSe. For the monolayer, DFT typically yields a larger band-gap energy than for bulk GeSe but cannot conclusively determine if the monolayer has a direct or indirect gap. Moreover, the DFT-optimized lattice parameters and atomic coordinates for monolayer GeSe depend strongly on the choice of approximation for the exchange-correlation functional, which makes the ideal structure-and its electronic properties-unclear. In order to obtain accurate lattice parameters and atomic coordinates for the monolayer, we use a surrogate Hessian-based parallel line search within diffusion Monte Carlo to fully optimize the GeSe monolayer structure. The DMC-optimized structure is different from those obtained using DFT, as are calculated band gaps. The potential energy surface has a shallow minimum at the optimal structure. This, combined with the sensitivity of the electronic structure to strain, suggests that the optical properties of monolayer GeSe are highly tunable by strain.

36 MATERIALS SCIENCE↗

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↗