Limited-memory Broyden Fletcher Goldfarb Shanno Algorithm Research Articles

Optimizing Parameter Efficiency in Machine Learning Models: A Focus on Reducing Memory Overhead with L-BFGS-Optimized Algorithms

This research addresses the critical challenge of detecting cotton leaf diseases through an advanced image processing and machine learning approach. The study primarily focuses on the extraction of significant features from cotton leaf images to facilitate accurate disease identification. The novelty of this work lies in the application of the Limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) algorithm for optimizing Support Vector Machines (SVM), enhancing the precision of disease detection in cotton leaves. This research method involves a comprehensive process of acquiring high-resolution leaf images, followed by an effective feature extraction technique that isolates crucial characteristics indicative of various plant diseases. Subsequently, these features are employed to train an SVM model optimized by the L-BFGS algorithm, a decision process that marks a significant departure from traditional gradient descent methods in SVM training. A pivotal aspect of this study is the comparative analysis conducted between the proposed L-BFGS-optimized SVM model and prevalent machine learning models including Random Forest, Decision Tree, Regression Models, and K-Nearest Neighbors (KNN). This comparison is grounded on various performance metrics such as accuracy, precision, recall, and F1-score, offering a comprehensive evaluation of each model's effectiveness in disease detection. The results of this research are expected to demonstrate the superiority of the L-BFGS-optimized SVM in terms of accuracy and efficiency in detecting cotton leaf diseases. This advancement holds substantial promise for agricultural technology, potentially leading to more informed and timely decision-making in crop management and disease prevention. The findings of this study aim to contribute significantly to the field of agricultural informatics, particularly in the domain of plant disease detection and management, by providing a more robust, accurate, and efficient tool for farmers and agriculturalists.

A Combined Approach for Predicting the Distribution of Harmful Substances in the Atmosphere Based on Parameter Estimation and Machine Learning Algorithms

This paper proposes a new approach to predicting the distribution of harmful substances in the atmosphere based on the combined use of the parameter estimation technique and machine learning algorithms. The essence of the proposed approach is based on the assumption that the concentration values predicted by machine learning algorithms at observation points can be used to refine the pollutant concentration field when solving a differential equation of the convection-diffusion-reaction type. This approach reduces to minimizing an objective functional on some admissible set by choosing the atmospheric turbulence coefficient. We consider two atmospheric turbulence models and restore its unknown parameters by using the limited-memory Broyden–Fletcher–Goldfarb–Shanno algorithm. Three ensemble machine learning algorithms are analyzed for the prediction of concentration values at observation points, and comparison of the predicted values with the measurement results is presented. The proposed approach has been tested on an example of two cities in the Republic of Kazakhstan. In addition, due to the lack of data on pollution sources and their intensities, an approach for identifying this information is presented.

Fast High-Resolution Phase Diversity Wavefront Sensing with L-BFGS Algorithm

The presence of manufacture error in large mirrors introduces high-order aberrations, which can severely influence the intensity distribution of point spread function. Therefore, high-resolution phase diversity wavefront sensing is usually needed. However, high-resolution phase diversity wavefront sensing is restricted with the problem of low efficiency and stagnation. This paper proposes a fast high-resolution phase diversity method with limited memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) algorithm, which can accurately detect aberrations in the presence of high-order aberrations. An analytical gradient of the objective function for phase-diversity is integrated into the framework of the L-BFGS nonlinear optimization algorithm. L-BFGS algorithm is specifically suitable for high-resolution wavefront sensing where a large phase matrix is optimized. The performance of phase diversity with L-BFGS is compared to other iterative method through simulations and a real experiment. This work contributes to fast high-resolution image-based wavefront sensing with a high robustness.

Multi-depth phase-only hologram optimization using the L-BFGS algorithm with sequential slicing.

We implement a limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) optimization of phase-only computer-generated hologram for a multi-depth three-dimensional (3D) target. Instead of computing the full 3D reconstruction of the hologram, we use a novel method using L-BFGS with sequential slicing (SS) for partial evaluation of the hologram during optimization that only computes loss for a single slice of the reconstruction at every iteration. We demonstrate that its ability to record curvature information enables L-BFGS to have good quality imbalance suppression under the SS technique.

Comparison of Different Weight Optimization Algorithm in Neural Network to Predict Mechanical Properties of AAC Lightweight Brick

This research aims to find the optimal weight optimization algorithm and number of hidden nodes that can be used in Artificial Neural Network to predict mechanical properties (density and compressive strength) of Autoclaved Aerated Concrete (AAC) lightweight brick. The dataset is obtained from secondary source, with a total of 51 data points. From this dataset, the relationship between constituent elements of AAC with its density and compressive strength is modeled using ANN. It was found that the best weight optimization algorithm that can be used for this dataset is the LBFGS (Limited-memory Broyden–Fletcher–Goldfarb–Shanno) algorithm. The optimum hidden layer node is found to be 90 nodes. With this parameters, the ANN can predict density and compressive strength of AAC lightweight brick with accuracy of 93.51% and margin of error around 6.49%. The accuracy of the prediction can be improved by appending the dataset with data points from secondary sources or by doing more experiments and tests.

Data-driven techniques for temperature data prediction: big data analytics approach

For extrapolation, climate change and other meteorological analysis, a study of past and current weather events is a prerequisite. NASA (National Aeronautics and Space Administration) has been able to develop a model capable of predicting various weather data for any location on the Earth, including locations lacking weather stations, weather satellite coverage, and other weather measuring instruments. This paper evaluates the prediction accuracy of the NASA temperature data with respect to NiMet (Nigerian Meteorological Agency) ground truth measurement, using Akwa Ibom Airport as a case study. Exploratory data analysis (descriptive and diagnostic analyses) of temperature retrieved from NiMet and NASA was performed to give a clear path to follow for predictive and prescriptive analyses. Using 2783days of weather data retrieved from NiMet as ground truth, the accuracy of NASA predictions with the corresponding resolution was calculated. Mean absolute error (MAE) of 2.184°C and root mean square error (RMSE) of 2.579°C, with a coefficient of determination (R2) of 0.710 for maximum temperature, then MAE of 0.876°C, RMSE of 1.225°C with a coefficient of determination (R2) of 0.620 for minimum temperature was discovered. There is a good correlation between the two datasets; hence, a model can be developed to generate more accurate predictions, using the NASA data as input. Predictive and prescriptive analyses were performed by employing five prediction algorithms: decision tree regression, XGBoost regression and MLP (multilayer perceptron) with LBFGS (limited-memory Broyden-Fletcher-Goldfarb-Shanno) optimizer, MLP with SGD (stochastic gradient) optimizer and MLP with Adam optimizer. The MLP LBFGS algorithm performed best, by significantly reducing the MAE by 35.35% and RMSE by 31.06% for maximum temperature, accordingly, MAE by 10.05% and RMSE by 8.00% for minimum temperature. Results obtained show that given sufficient data, plugging NASA predictions as input to an LBFGS-MLP model gives more accurate temperature predictions for the study area.

Cryogenic energy storage: Standalone design, rigorous optimization and techno-economic analysis

Energy storage allows flexible use and management of excess electricity and intermittently available renewable energy. Cryogenic energy storage (CES) is a promising storage alternative with a high technology readiness level and maturity, but the round-trip efficiency is often moderate and the Levelized Cost of Storage (LCOS) remains high. The complex flowsheets with intricate thermodynamics at cryogenic temperatures as well as the presence of multiple loops and refrigeration cycles pose considerable challenges for rigorous model-based design and optimization of CES systems. We present an optimization strategy that couples rigorous process simulation and Bayesian optimization with flowsheet decomposition and identification of hidden coupling constraints to optimally design standalone CES systems. Further refinement is done via a local search using the limited-memory Broyden–Fletcher–Goldfarb–Shanno algorithm. Our results indicate that it is possible to achieve more than 52% round-trip efficiency and an LCOS of $153/MWh for a standalone 100 MW/400 MWh CES system limited to short-term storage with daily charging–discharging. However, a detailed techno-economic assessment reveals that the LCOS considering total capital investment may exceed $267/MWh when all direct and indirect costs of installation and operation are considered.

LOMETS3: integrating deep learning and profile alignment for advanced protein template recognition and function annotation.

Deep learning techniques have significantly advanced the field of protein structure prediction. LOMETS3 (https://zhanglab.ccmb.med.umich.edu/LOMETS/) is a new generation meta-server approach to template-based protein structure prediction and function annotation, which integrates newly developed deep learning threading methods. For the first time, we have extended LOMETS3 to handle multi-domain proteins and to construct full-length models with gradient-based optimizations. Starting from a FASTA-formatted sequence, LOMETS3 performs four steps of domain boundary prediction, domain-level template identification, full-length template/model assembly and structure-based function prediction. The output of LOMETS3 contains (i) top-ranked templates from LOMETS3 and its component threading programs, (ii) up to 5 full-length structure models constructed by L-BFGS (limited-memory Broyden–Fletcher–Goldfarb–Shanno algorithm) optimization, (iii) the 10 closest Protein Data Bank (PDB) structures to the target, (iv) structure-based functional predictions, (v) domain partition and assembly results, and (vi) the domain-level threading results, including items (i)–(iii) for each identified domain. LOMETS3 was tested in large-scale benchmarks and the blind CASP14 (14th Critical Assessment of Structure Prediction) experiment, where the overall template recognition and function prediction accuracy is significantly beyond its predecessors and other state-of-the-art threading approaches, especially for hard targets without homologous templates in the PDB. Based on the improved developments, LOMETS3 should help significantly advance the capability of broader biomedical community for template-based protein structure and function modelling.

Fast sparse image reconstruction method in through-the-wall radars using limited memory Broyden–Fletcher–Goldfarb–Shanno algorithm

AbstractCompressed sensing allows recovery of image signals using a portion of data – a technique that has drastically revolutionized the field of through-the-wall radar imaging (TWRI). This technique can be accomplished through nonlinear methods, including convex programming and greedy iterative algorithms. However, such (nonlinear) methods increase the computational cost at the sensing and reconstruction stages, thus limiting the application of TWRI in delicate practical tasks (e.g. military operations and rescue missions) that demand fast response times. Motivated by this limitation, the current work introduces the use of a numerical optimization algorithm, called Limited Memory Broyden–Fletcher–Goldfarb–Shanno (LBFGS), to the TWRI framework to lower image reconstruction time. LBFGS, a well-known Quasi-Newton algorithm, has traditionally been applied to solve large scale optimization problems. Despite its potential applications, this algorithm has not been extensively applied in TWRI. Therefore, guided by LBFGS and using the Euclidean norm, we employed the regularized least square method to solve the cost function of the TWRI problem. Simulation results show that our method reduces the computational time by 87% relative to the classical method, even under situations of increased number of targets or large data volume. Moreover, the results show that the proposed method remains robust when applied to noisy environment.

ML-descent: An optimization algorithm for full-waveform inversion using machine learning

Full-waveform inversion (FWI) is a nonlinear optimization problem, and a typical optimization algorithm such as the nonlinear conjugate gradient or limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) would iteratively update the model mainly along the gradient-descent direction of the misfit function or a slight modification of it. Based on the concept of meta-learning, rather than using a hand-designed optimization algorithm, we have trained the machine (represented by a neural network) to learn an optimization algorithm, entitled the “ML-descent,” and apply it in FWI. Using a recurrent neural network (RNN), we use the gradient of the misfit function as the input, and the hidden states in the RNN incorporate the history information of the gradient similar to an LBFGS algorithm. However, unlike the fixed form of the LBFGS algorithm, the machine-learning (ML) version evolves in response to the gradient. The loss function for training is formulated as a weighted summation of the L2 norm of the data residuals in the original inverse problem. As with any well-defined nonlinear inverse problem, the optimization can be locally approximated by a linear convex problem; thus, to accelerate the training, we train the neural network by minimizing randomly generated quadratic functions instead of performing time-consuming FWIs. To further improve the accuracy and robustness, we use a variational autoencoder that projects and represents the model in latent space. We use the Marmousi and the overthrust examples to demonstrate that the ML-descent method shows faster convergence and outperforms conventional optimization algorithms. The energy in the deeper part of the models can be recovered by the ML-descent even when the pseudoinverse of the Hessian is not incorporated in the FWI update.

A Frequency-Domain Quasi-Newton-Based Biparameter Synchronous Imaging Scheme for Ground-Penetrating Radar With Applications in Full Waveform Inversion

Full waveform inversion (FWI) of ground-penetrating radar (GPR) data is becoming a promising technique to facilitate the interpretation of surface-GPR data and the mapping of the subsurface. However, more general FWIs still require a sufficient amount of RAM memory, and it is difficult to produce an accurate and representative reconstruction result due to a large amount of the Hessian matrix calculations and singular value decomposition (SVD). In this article, we developed a novel full-waveform approach of the limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) algorithm for surface-GPR data that is based on a quasi-Newton framework and the total variation (TV) regularization. The proposed approach uses an L-BFGS algorithm and combines a scale-transformation regularization technique to mitigate the ill-posed problem of inversion, which can impose a biparameter preinformation constraint to ensure the stability of inversion, and adaptive regularization weights are applied to improve the convergence efficiency of inversion. To demonstrate the novelty and effectiveness of the proposed scheme, we tested our FWI algorithm using synthetic data and in-site field data. In the testing, we focus on analyzing the influence of different aspects of the FWI results, including different scale factors, regularization weights, inversion strategies, acquisition configurations, initial models, and the noisy data set. In particular, the FWI experiment is performed to demonstrate the applicability of the proposed algorithm. The results show that the proposed algorithm can effectively reconstruct the biparameter near the subsurface with high accuracy, which makes our approach very attractive for attribute analysis applications and makes the surface-GPR FWI commercially viable.

Three-dimensional magnetotelluric inversion using L-BFGS

The gradient-based optimization methods are preferable for the large-scale three-dimensional (3D) magnetotelluric (MT) inverse problem. Compared with the popular nonlinear conjugate gradient (NLCG) method, however, the limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) method is less adopted. This paper aims to implement a L-BFGS-based inversion algorithm for the 3D MT problem. And we develop our code on top of the ModEM package, which is highly extensible and popular among the MT community. To accelerate the convergence speed, the preconditioning technique by the affine linear transformation of the original model parameters is used. Two modifications of the conventional L-BFGS algorithm are also made to get a comparable convergence rate with the NLCG method. The impacts of the preconditioner parameters, the regularization parameters, the starting model, etc., on the inversion are evaluated by synthetic examples for both L-BFGS and NLCG methods. And the real MT Kayabe dataset is also inverted by the inversion algorithms. The synthetic tests show that through our L-BFGS inversion algorithm the similar resistivity models can be obtained with that from the NLCG method. For the real data inversion, the L-BFGS method performs more efficiently and reasonable results could be obtained by less iterations of the inversion process than the NLCG method. Thus, we suggest the common usage of the L-BFGS method for the 3D MT inverse problem.

Hybrid reconstruction method for multispectral bioluminescence tomography with log-sum regularization.

Bioluminescence tomography (BLT) has important applications in the in vivo visualization of a pathological process for preclinical studies. However, the reconstruction of BLT is severely ill-posed. To recover the bioluminescence source stably and efficiently, we use a log-sum regularization term in the objective function and utilize a hybrid optimization algorithm for solving the nonconvex regularized problems (HONOR). The hybrid optimization scheme of HONOR merges second-order information and first-order information to reconstruction by choosing either the quasi-Newton (QN) or gradient descent step at each iteration. The QN step uses the limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm (L-BFGS) to acquire second-order information. Simulations and in vivo experiments based on multispectral measurements demonstrated the remarkable performance of the proposed hybrid method in the sparse reconstruction of BLT.

Hybrid modelling routine for metal‐oxide TFTs based on particle swarm optimisation and artificial neural network

An effective and robust hybrid algorithm consisting of particle swarm optimisation (PSO) and limited memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) method based on artificial neural network (ANN) is proposed for modelling flexible metal-oxide thin-film transistors (TFTs). The L-BFGS method as an optimiser is exploited to update the parameters of ANN and speed up the training process. A mutation strategy for PSO is derived to enhance the searching ability further. With the great global searching ability, PSO is implemented to find a hopeful initial position in solution space for the next ANN model. The simulation result shows a high accuracy not only in I–V curve fitting but also in small-signal parameter ( g m , g d , etc.) predictions, which have not been exposed in the training process. The measured DC characteristics of In–Zn–O TFTs are used to verify the proposed ANN model, which has the benefits of rapid fitting from the L-BFGS algorithm and universal searching ability from PSO.

Multi-label Log-Loss function using L-BFGS for document categorization

Text mining, which fundamentally involves quantitative tactics to analyze textual data, can be used for discovering knowledge and to achieve scholarly research goals. For large-scale data such as corpus text, intelligent learning methods have been effectively approached. In this paper, an artificial neural network with a quasi-Newton updating procedure is presented for multi-label multi-class text classification. This numerical unconstrained training technique, the Multi-Label extension of Log-Loss function using in Limited-memory Broyden–Fletcher–Goldfarb–Shanno algorithm (ML4BFGS), provides a noteworthy opportunity for text mining and leads to a significant improvement in text classification performances. The ML4BFGS training approach is applied to allocate some (one or multi) of the classes to each corresponding sentence from different available labels. We evaluate this method on English translations of the Holy Quran. These religious texts have been chosen for experiments of this manuscript because each verse (sentence) usually has multiple labels (topics) and different translations of each verse should have the same labels. Experimental results show that ML4BFGS is talented for multi-label multi-class classification in the Quranic corpus. Evaluation criteria of some advanced updating methods such as ITCG, BFGS, L-BFGS-B, L3BFGS as well as some other multi-label approaches such as ML-k-NN, and well-known SVM are compared with the proposed ML4BFGS and the outcomes are fully-described in this study. The performance measures including the Hamming loss, recall, precision, and F1 score show that the ML4BFGS achieves the best results in extracting related classes for each verse, while the proposed network takes the least epochs compared to the other training approach for completing learning or training phase. Simultaneously, the elapsed time for ML4BFGS is just 78% (in seconds) of the best experience of this term. Compared with the applicability of some state-of-the-art algorithms, ML4BFGS has a less computational cost, faster convergence rate, and much accuracy in corpus analysis.

Transformation from total-field magnetic anomaly to the projection of the anomalous vector onto the normal geomagnetic field based on an optimization method

The total-field magnetic anomaly [Formula: see text] is approximated as the component [Formula: see text] of the anomalous vector [Formula: see text] along the direction of the normal geomagnetic field. It is widely used in magnetic data processing and interpretation practices as a routine if [Formula: see text] is relatively small. But in highly magnetic environments, the distinction between [Formula: see text] and [Formula: see text] is often too large to be ignored. We carefully investigate the difference between [Formula: see text] and [Formula: see text] and find that it will increase rapidly in the trend of the quadratic function as [Formula: see text] strengthens. We also test the effects of approximation on the component transformation and reduction to the pole on a synthetic single-sphere model. As expected, the error caused by inaccurate information will propagate into subsequent data processing procedures and adversely affect the results. Therefore, we have developed an optimization strategy based on the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm to transform the total-field anomaly into [Formula: see text]. First, we have constructed an objective function after transforming [Formula: see text] into [Formula: see text] through the component transformation in the frequency domain. Then, using [Formula: see text] as the initial value of [Formula: see text], [Formula: see text] is calculated iteratively by the L-BFGS algorithm. To test the validity of the optimization algorithm, [Formula: see text] is transformed for noise-free and noise-corrupted models and models with a background field. The synthetics indicate that the transformed [Formula: see text] is almost the same as the model [Formula: see text], whose maximum error is approximately one-hundredth (30 nT) of the difference (8000 nT) between the modeled [Formula: see text] and [Formula: see text]. The synthetics and field data example from the Yangshan Iron Mine, Fujian Province, southern China, also indicate that the data transformation and forward-modeling results can benefit from the direct use of transformed [Formula: see text] instead of [Formula: see text].

Land surface model parameter optimisation using in situ flux data: comparison of gradient-based versus random search algorithms (a case study using ORCHIDEE v1.9.5.2)

Abstract. Land surface models (LSMs), which form the land component of earth system models, rely on numerous processes for describing carbon, water and energy budgets, often associated with highly uncertain parameters. Data assimilation (DA) is a useful approach for optimising the most critical parameters in order to improve model accuracy and refine future climate predictions. In this study, we compare two different DA methods for optimising the parameters of seven plant functional types (PFTs) of the ORCHIDEE LSM using daily averaged eddy-covariance observations of net ecosystem exchange and latent heat flux at 78 sites across the globe. We perform a technical investigation of two classes of minimisation methods – local gradient-based (the L-BFGS-B algorithm, limited memory Broyden–Fletcher–Goldfarb–Shanno algorithm with bound constraints) and global random search (the genetic algorithm) – by evaluating their relative performance in terms of the model–data fit and the difference in retrieved parameter values. We examine the performance of each method for two cases: when optimising parameters at each site independently (“single-site” approach) and when simultaneously optimising the model at all sites for a given PFT using a common set of parameters (“multi-site” approach). We find that for the single site case the random search algorithm results in lower values of the cost function (i.e. lower model–data root mean square differences) than the gradient-based method; the difference between the two methods is smaller for the multi-site optimisation due to a smoothing of the cost function shape with a greater number of observations. The spread of the cost function, when performing the same tests with 16 random first-guess parameters, is much larger with the gradient-based method, due to the higher likelihood of being trapped in local minima. When using pseudo-observation tests, the genetic algorithm results in a closer approximation of the true posterior parameter value in the L-BFGS-B algorithm. We demonstrate the advantages and challenges of different DA techniques and provide some advice on using it for the LSM parameter optimisation.

Large-scale distributed L-BFGS

With the increasing demand for examining and extracting patterns from massive amounts of data, it is critical to be able to train large models to fulfill the needs that recent advances in the machine learning area create. L-BFGS (Limited-memory Broyden Fletcher Goldfarb Shanno) is a numeric optimization method that has been effectively used for parameter estimation to train various machine learning models. As the number of parameters increase, implementing this algorithm on one single machine can be insufficient, due to the limited number of computational resources available. In this paper, we present a parallelized implementation of the L-BFGS algorithm on a distributed system which includes a cluster of commodity computing machines. We use open source HPCC Systems (High-Performance Computing Cluster) platform as the underlying distributed system to implement the L-BFGS algorithm. We initially provide an overview of the HPCC Systems framework and how it allows for the parallel and distributed computations important for Big Data analytics and, subsequently, we explain our implementation of the L-BFGS algorithm on this platform. Our experimental results show that our large-scale implementation of the L-BFGS algorithm can easily scale from training models with millions of parameters to models with billions of parameters by simply increasing the number of commodity computational nodes.

Hadoop Recognition of Biomedical Named Entity Using Conditional Random Fields

Processing large volumes of data has presented a challenging issue, particularly in data-redundant systems. As one of the most recognized models, the conditional random fields (CRF) model has been widely applied in biomedical named entity recognition (Bio-NER). Due to the internally sequential feature, performance improvement of the CRF model is nontrivial, which requires new parallelized solutions. By combining and parallelizing the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) and Viterbi algorithms, we propose a parallel CRF algorithm called MapReduce CRF (MRCRF) in this paper, which contains two parallel sub-algorithms to handle two time-consuming steps of the CRF model. The MapReduce L-BFGS (MRLB) algorithm leverages the MapReduce framework to enhance the capability of estimating parameters. Furthermore, the MapReduce Viterbi (MRVtb) algorithm infers the most likely state sequence by extending the Viterbi algorithm with another MapReduce job. Experimental results show that the MRCRF algorithm outperforms other competing methods by exhibiting significant performance improvement in terms of time efficiency as well as preserving a guaranteed level of correctness.

Stabilized quasi-Newton optimization of noisy potential energy surfaces.

Optimizations of atomic positions belong to the most commonly performed tasks in electronic structure calculations. Many simulations like global minimum searches or characterizations of chemical reactions require performing hundreds or thousands of minimizations or saddle computations. To automatize these tasks, optimization algorithms must not only be efficient but also very reliable. Unfortunately, computational noise in forces and energies is inherent to electronic structure codes. This computational noise poses a severe problem to the stability of efficient optimization methods like the limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm. We here present a technique that allows obtaining significant curvature information of noisy potential energy surfaces. We use this technique to construct both, a stabilized quasi-Newton minimization method and a stabilized quasi-Newton saddle finding approach. We demonstrate with the help of benchmarks that both the minimizer and the saddle finding approach are superior to comparable existing methods.