Nonlinear Optimization Techniques Research Articles

Alignment of a 360° image with posed color images for locally accurate texturing of 3D mesh

With the popularity of 3D content like virtual tours, the challenges of 3D data registration have become increasingly significant. The registration of heterogeneous data obtained from 2D and 3D sensors is required to create photo-realistic 3D models. However, the alignment of 2D images with 3D models introduces a significant challenge due to their inherent differences. This article introduces a rigorous mathematical approach to align a 360° image with its corresponding 3D model generated from images with known camera poses followed by texture projection on the model. We use Scale-Invariant Feature Transform (SIFT) feature descriptors enhanced with a homography-based metric to establish correspondences between the faces of a cubemap and the posed images. To achieve optimal alignment, we use a non-linear least squares optimization technique with a custom objective function. Subsequently, the outcomes of the alignment process are evaluated through texturing using a customized raytracing algorithm. The resulting projections are compared against the original textures, with a comprehensive assessment of the alignment's fidelity and precision.

A Sustainable Inventory Model with Advertisement Effort for Imperfect Quality Items under Learning in Fuzzy Monsoon Demand

In this paper, we proposed a sustainable inventory model with a learning effect for imperfect quality items under different kinds of fuzzy environments like crisp, general fuzzy, cloudy fuzzy, and monsoon fuzzy. We divided the mathematical model into three parts under the learning effect according to the real-time fuzzy components (crisp, cloudy, and monsoon environments) of the demand rate of the items. We minimized the total inventory cost with respect to cycle length in each environment under the proposed assumptions. The non-linear optimization technique is applied for the algorithm and the solution method to find the decision variable. Finally, we compared the total inventory cost under different fuzzy environments and our finding is that the fuzzy monsoon environment is a more effective fuzzy environment than crisp and cloudy fuzzy environments. We have presented a numerical example for the validation of the proposed model and have shown the impact of the inventory input parameters on the cycle length and total inventory fuzzy cost. The managerial insights and future scope of this proposed study have been shown in the sensitivity analysis and conclusion. The limitations, application, future extension and scope, and social implementation have been shown in this research study.

Integration of Complex Mathematical Approaches and Statistical Methodologies in Machine Learning for Design of Robust Prediction Models

The disease known as breast cancer continues to be one of the most common and potentially fatal diseases that affect women all over the world. In order to provide effective therapy and more favorable outcomes for patients, early detection and correct diagnosis are absolutely necessary. This research explores the integration of operational research (OR) methodologies and advanced statistical methods within machine learning frameworks to enhance the prediction accuracy of breast cancer outcomes. By harnessing the power of nonlinear optimization and statistical techniques, including regression analysis and probability distribution models, we aim to refine the predictive capabilities of existing algorithms. The research employs a comprehensive dataset derived from clinical trials and patient records, analyzed through a series of machine learning models that incorporate elements of combinatorial optimization, decision analysis, and stochastic modeling. Key performance metrics, such as accuracy, sensitivity, and specificity, are evaluated against standard benchmarks to determine the efficacy of the integrated approaches. Preliminary results indicate that incorporating OR and statistical methods significantly improves model robustness and predictive accuracy. The study not only demonstrates the potential of applied mathematics in medical diagnostics but also provides a framework for future research in enhancing machine learning models for health outcomes prediction through mathematical innovations. This investigation contributes to the field of mathematical oncology by demonstrating how applied nonlinear analysis can bridge the gap between theoretical mathematical approaches and practical clinical applications, offering new pathways for early and more accurate detection of breast cancer.

Characterizing Lossy Dielectric Materials in Shock Physics by Millimeter-Wave Interferometry Using One-Dimensional Convolutional Neural Networks and Nonlinear Optimization

When a dielectric material undergoes mechanical impact, it generates a shock wave, causing changes in its refractive index. Recent demonstrations have proven that the modified refractive index can be determined remotely using a millimeter-wave interferometer. However, these demonstrations are based on the resolution of an inverse electromagnetic problem, which assumes that the losses in the material are negligible. This restrictive assumption is overcome in this article, in which a new approach is proposed to solve the inverse electromagnetic problem in lossy and shocked dielectric materials. Our methodology combines a one-dimensional convolutional neural network architecture, namely Inverse problem of Lossless or Lossy Shocked Wavefront Network (ILSW-Net), with a nonlinear optimization technique based on the Nelder–Mead algorithm to estimate losses within dielectric materials under a mechanical impact. Experimental results for both simulated and real signals show that our method can successfully predict the velocities and the refractive index while accurately estimating the shock wavefront.

A metaheuristic particle swarm optimization for enhancing energetic and exergetic performances of hydrogen energy production from plastic waste gasification

In recent decades, there has been a surge in demand for the development of renewable energies, leading to extensive research efforts focused on the gasification process. Consequently, a wide range of studies has been conducted to explore different feedstocks for gasification, with particular emphasis on plastic waste. Although a wide range of studies conducted various optimization methods for the gasification process, there was no specific study to employ metaheuristic methods in the field of plastic waste gasification. This study aimed to perform a multi-objective particle swarm optimization (MOPSO) method to solve a multi-objective plastic waste gasification optimization problem for enhancing energetic and exergetic viewpoints. Moreover, exact methods including non-linear optimization and response surface methodology (RSM) were conducted to be compared with the results derived from MOPSO. Pareto-front solutions obtained from MOPSO were ranked using grey relational analysis (GRA) and the optimum responses were 517 kJ/kg, 84 %, and 57 % for lower-heating value, cold gas efficiency, and exergy efficiency, respectively, which were compared to optimum options obtained from multi-objective non-linear optimization and RSM techniques. While the MOPSO model may not have performed as well as other methods in this particular problem, it is important to acknowledge its capabilities. Future research can concentrate on improving the behavior and performance of the MOPSO method when dealing with a larger number of points or when applied to different problem domains.

Modeling and Calibration of Gaia, Hipparcos, and Tycho-2 Astrometric Data for the Detection of Dark Companions

Hidden within the Gaia satellite’s multiple data releases lies a valuable cache of dark companions. To facilitate the efficient and reliable detection of these companions via combined analyses involving the Gaia, Hipparcos, and Tycho-2 catalogs, we introduce an astrometric modeling framework. This method incorporates analytical least-square minimization and nonlinear parameter optimization techniques to a set of common calibration sources across the different space-based astrometric catalogs. This enables us to discern the error inflation, astrometric jitter, differential parallax zero-points, and frame rotation of various catalogs relative to Gaia Data Release 3 (DR3). Our findings yield the most precise Gaia DR2 calibration parameters to date, revealing notable dependencies on magnitude and color. Intriguingly, we identify submilliarcsecond frame rotation between Gaia DR1 and DR3, along with an estimated astrometric jitter of 2.16 mas for the revised Hipparcos catalog. In a thorough comparative analysis with previous studies, we offer recommendations on calibrating and utilizing different catalogs for companion detection. Furthermore, we provide a user-friendly pipeline (https://github.com/ruiyicheng/Download_HIP_Gaia_GOST) for catalog download and bias correction, enhancing accessibility and usability within the scientific community.

Controlled random initialization of search vectors for application of gravitational search algorithm to selective harmonic elimination PWM

The prime objective of SHE PWM is to eliminate selected lower order harmonic by solving a set of non-linear transcendental equation while maintaining the fundamental component at a desired satisfactory value. In order to solve these non-linear equations different metaheuristic optimization techniques has been used in recent past. Due to faster convergence rate increased precision and higher probability to calculus based mathematical approximation techniques. In this manuscript an improved initialized Gravitational search algorithm has been proposed for a uni-polar 3-phase inverter. The algorithm is improved upon through a controlled random initialization of search agent, specifically for the purpose of solving the set of non-linear transcendental equation in SHEPWM for 3- switching angles. The simulation of the gravitational search algorithm and the proposed improved initialized GSA has been performed in MATLAB software and comparison of different performance parameter like Harmonic distortion, convergence rate etc. has been studied. The simulation results proves that a considerable improvement has been achieved by applying improved initialized GSA algorithm in terms of harmonic mitigation, convergence rate and accuracy in finding out the appropriate switching angles. Finally, the results obtained in simulation are verified through an appropriate experimental setup.

Likelihood-free posterior estimation and uncertainty quantification for diffusion MRI models

Abstract Diffusion magnetic resonance imaging (dMRI) allows to estimate brain tissue microstructure as well as the connectivity of the white matter (known as tractography). Accurate estimation of the model parameters (by solving the inverse problem) is thus very important to infer the underlying biophysical tissue properties and fiber orientations. Although there has been extensive research on this topic with a myriad of dMRI models, most models use standard nonlinear optimization techniques and only provide an estimate of the model parameters without any information (quantification) about uncertainty in their estimation. Further, the effect of this uncertainty on the estimation of the derived dMRI microstructural measures downstream (e.g., fractional anisotropy) is often unknown and is rarely estimated. To address this issue, we first design a new deep-learning algorithm to identify the number of crossing fibers in each voxel. Then, at each voxel, we propose a robust likelihood-free deep learning method to estimate not only the mean estimate of the parameters of a multi-fiber dMRI model (e.g., the biexponential model), but also its full posterior distribution. The posterior distribution is then used to estimate the uncertainty in the model parameters as well as the derived measures. We perform several synthetic and in-vivo quantitative experiments to demonstrate the robustness of our approach for different noise levels and out-of-distribution test samples. Besides, our approach is computationally fast and requires an order of magnitude less time than standard nonlinear fitting techniques. The proposed method demonstrates much lower error (compared to existing methods) in estimating several metrics, including number of fibers in a voxel, fiber orientation, and tensor eigenvalues. The proposed methodology is quite general and can be used for the estimation of the parameters from any other dMRI model.

Research on Piano Curriculum Education and Its Performance Ecosystem Based on Network Flow Optimization

Abstract This paper investigates music education, where an efficient and accurate performance evaluation system in the piano teaching and performance ecosystem is increasingly becoming an essential tool for improving teaching quality and performance level. The objective evaluation of students’ performance skills can be achieved by carefully analyzing piano performances using the network flow optimization technique. This technique optimizes the performance evaluation system’s audio recognition ability by analyzing the piano audio signal and solving the multi-constraint nonlinear optimization problem in a limited time domain. This paper establishes a network flow optimization model, applies the multi-constraint nonlinear optimization technique, and combines the non-negative matrix decomposition and dynamic time regularization algorithm to analyze the piano performance for experiments. After optimization processing, hundreds of piano audio samples were collected, and the audio recognition accuracy was improved by 20%. By optimizing and processing the audio signals from the network stream, the evaluation system could detect polyphony more accurately and track the musical score effectively, improving accuracy and efficiency. Using the non-negative matrix decomposition algorithm, the accuracy of detecting polyphony can reach 85%, while the dynamic temporal regularization algorithm can match the position of the musical score with 95% accuracy. The accuracy of piano performance evaluation is optimized by this network flow optimization method, providing new technical means for music education, and promoting the quality of teaching and performance.

An Overview of Mathematical Methods Applied in the Biomechanics of Foot and Ankle–Foot Orthosis Models

Ankle–foot orthoses (AFOs) constitute medical instruments designed for patients exhibiting pathological gait patterns, notably stemming from conditions such as stroke, with the primary objective of providing support and facilitating rehabilitation. The present research endeavors to conduct a comprehensive review of extant scholarly literature focusing on mathematical techniques employed for the examination of AFO models. The overarching aim is to gain deeper insights into the biomechanical intricacies underlying these ankle–foot orthosis models from a mathematical perspective, while concurrently aiming to advance novel models within the domain. Utilizing a specified set of keywords and their configurations, a systematic search was conducted across notable academic databases, including ISI Web of Knowledge, Google Scholar, Scopus, and PubMed. Subsequently, a total of 23 articles were meticulously selected for in-depth review. These scholarly contributions collectively shed light on the utilization of nonlinear optimization techniques within the context of ankle–foot orthoses (AFOs), specifically within the framework of fully Cartesian coordinates, encompassing both kinematic and dynamic dimensions. Furthermore, an exploration of a two-degree-of-freedom AFO design tailored for robotic rehabilitation, which takes into account the interplay between foot and orthosis models, is delineated. Notably, the review article underscores the incorporation of shape memory alloy (SMA) elements in AFOs and overviews the constitutive elastic, viscoelastic, and hyperelastic models. This comprehensive synthesis of research findings stands to provide valuable insights for orthotists and engineers, enabling them to gain a mathematical understanding of the biomechanical principles underpinning AFO models and fostering the development of innovative AFO designs.

Mathematical Camera Array Optimization for Face 3D Modeling Application.

Camera network design is a challenging task for many applications in photogrammetry, biomedical engineering, robotics, and industrial metrology, among other fields. Many driving factors are found in the camera network design including the camera specifications, object of interest, and type of application. One of the interesting applications is 3D face modeling and recognition which involves recognizing an individual based on facial attributes derived from the constructed 3D model. Developers and researchers still face difficulty in reaching the required high level of accuracy and reliability needed for image-based 3D face models. This is caused among many factors by the hardware limitations and imperfection of the cameras and the lack of proficiency in designing the ideal camera-system configuration. Accordingly, for precise measurements, we still need engineering-based techniques to ascertain the specific level of deliverables quality. In this paper, an optimal geometric design methodology of the camera network is presented by investigating different multi-camera system configurations composed of four up to eight cameras. A mathematical nonlinear constrained optimization technique is applied to solve the problem and each camera system configuration is tested for a facial 3D model where a quality assessment is applied to conclude the best configuration. The optimal configuration is found to be a 7-camera array, comprising a pentagon shape enclosing two additional cameras, offering high accuracy. For those who prioritize point density, a 9-camera array with a pentagon and quadrilateral arrangement in the X-Z plane is a viable choice. However, a 5-camera array offers a balance between accuracy and the number of cameras.

Safe and Adaptive 3-D Locomotion via Constrained Task-Space Imitation Learning

Bipedal locomotion has been widely studied in recent years, where passive safety (i.e., a biped rapidly brakes without falling) is deemed to be a pivotal problem. To realize safe 3-D walking, existing works resort to nonlinear optimization techniques based on simplified dynamics models, requiring hand-tuned reference trajectories. In this article, we propose to integrate safety constraints into constrained task-space imitation learning, endowing a humanoid robot with adaptive walking capability. Specifically, unlike previous work using nonlinear and coupled capturability dynamics, we first linearize the 3-D capture conditions using appropriate extreme values and then seamlessly incorporate them into constrained imitation learning. Furthermore, we propose novel heuristic rules to define control points, enabling adaptive locomotion learning. The resulting framework allows robots to learn locomotion skills from a few demonstrations efficiently and apply the learned skills to unseen 3-D scenarios while satisfying the constraints for passive safety. Unlike deep enforcement learning, our framework avoids the need of a large number of iterations or sim-to-real transfer. By virtue of the task-space adaptability, the proposed imitation learning framework can reuse collected demonstrations in a new robot platform. We validate our method by hardware experiments on Walker2 robot and simulations on COMAN robot.

A Comparison of Nonlinear Optimization Methods for Rosenbrock, Booth, and Matyas Functions

There is increasing interest in the application of nonlinear optimization techniques across a broad range of real-world problems that is linked to rapid advances in novel technologies and renewed interest in areas like sustainable development. While many algorithms for nonlinear optimization have been developed, they differ widely in their methods of convergence to the solution. Consequently, matching the function to be optimized with the right optimization algorithm is essential. To further explore this relationship, we studied two nonlinear optimization methods – the Nelder-Mead simplex method that only performs function evaluations and the quasi-Newton method which requires estimation of derivatives. These algorithms were used to find the global minima of the Rosenbrock, Booth, and Matyas functions from multiple starting points. The convergence paths for each starting point across both optimization methods for all 3 functions were visualized on contour plots. While convergence on the global minima was observed in all instances, our analysis indicated that the quasi-Newton method was consistently more efficient and needed fewer iterations than the Simplex method. This was especially pronounced for the Booth and Matyas functions where ~10-fold and 20-fold fewer iterations, respectively, were necessary for convergence. Our analysis reinforces the need to carefully match properties of the function being minimized with the performance characteristics of the optimization approach to obtain fast convergence on the global minimum.

Nonlinear Optimization Techniques for Signal Processing

Nonlinear Optimization Techniques for Signal Processing

Modeling and parameter identification for agricultural machines

AbstractA series of technical and social aspects have led the pressure to increase energy efficiency and reduce the level of environmental impact in agricultural production. Crop producers and equipment manufacturers have identified computerized assistance in operation management as an indispensable tool to optimize agricultural processes. A central place is occupied in this regard by the so called digital twins, computer models of a specific instance of an object or system, which are also capable of exchanging data with the physical counterpart and updating their state accordingly. The core of a digital twin is given by the digital mock‐up, or offline digital twin, that is the computer model of the system's physics. The goal of this work is to present the development of an offline digital twin for a novel gantry‐tractor type autonomous agricultural machine. The peculiarity of this system resides in its until now scarcely adopted mechanical design, and its ability to perform a range of processes by attaching different modules to its frame. After a brief introduction into the characteristics of a gantry‐type tractor and its role in the context of precision autonomous agriculture and controlled traffic farming, different components of the machine and dynamic phenomena are separately investigated and mathematically modeled. Particular focus is placed thereby on the study of the vehicle's longitudinal dynamics. Based on the software implementation of the mathematical models, the unknown parameters of the system model are estimated by means of nonlinear optimization techniques, using sensor data collected during field operation as the measurement reference. The accuracy of different estimation methods is then evaluated against experimental samples collected by sensors.

Novel Bayesian Inference-Based Approach for the Uncertainty Characterization of Zhang's Camera Calibration Method.

Camera calibration is necessary for many machine vision applications. The calibration methods are based on linear or non-linear optimization techniques that aim to find the best estimate of the camera parameters. One of the most commonly used methods in computer vision for the calibration of intrinsic camera parameters and lens distortion (interior orientation) is Zhang's method. Additionally, the uncertainty of the camera parameters is normally estimated by assuming that their variability can be explained by the images of the different poses of a checkerboard. However, the degree of reliability for both the best parameter values and their associated uncertainties has not yet been verified. Inaccurate estimates of intrinsic and extrinsic parameters during camera calibration may introduce additional biases in post-processing. This is why we propose a novel Bayesian inference-based approach that has allowed us to evaluate the degree of certainty of Zhang's camera calibration procedure. For this purpose, the a prioriprobability was assumed to be the one estimated by Zhang, and the intrinsic parameters were recalibrated by Bayesian inversion. The uncertainty of the intrinsic parameters was found to differ from the ones estimated with Zhang's method. However, the major source of inaccuracy is caused by the procedure for calculating the extrinsic parameters. The procedure used in the novel Bayesian inference-based approach significantly improves the reliability of the predictions of the image points, as it optimizes the extrinsic parameters.

Characterization of an isolated lactase enzyme produced by Bacillus licheniformis ALSZ2 as a potential pharmaceutical supplement for lactose intolerance.

Lactose intolerance is a widespread problem that affects people of many different races all over the world. The following pharmacological supplements can improve the lives of those who suffer from this issue. This work focused on lactase producer isolation and statistical design (Plackett-Burman, and BOX-Behnken) to maximize the effectiveness of environmental factors. A lactase-producing bacterium was chosen from a discovery of 100 strains in soil that had previously been polluted with dairy products. Plackett-Burman investigated fifteen variables. The most critical variables that lead to increased lactase synthesis are glucose, peptone, and magnesium sulfate (MgSO4). The ideal process conditions for the creation of lactase yield among the stated variables were then determined using a BOX-Benken design. To establish a polynomial quadratic relationship between the three variables and lactase activity, the Box-Behnken design level was used. The EXCEL-solver nonlinear optimization technique was used to predict the best form for lactase production. The ideal temperature and pH levels have been determined, both before and after the lactase purification process, to achieve the highest performance of isolated lactase. According to this study, Bacillus licheniformis is a perfect supply of the lactase enzyme (β -Galactosidase), It can be used as a product to assist people who have health issues due to lactose intolerance.

Recent Developments in Security-Constrained AC Optimal Power Flow: Overview of Challenge 1 in the ARPA-E Grid Optimization Competition

Intro to the ARPA-E Grid Optimization Competition In “Recent Developments in Security-Constrained AC Optimal Power Flow: Overview of Challenge 1 in the ARPA-E Grid Optimization Competition,” we review the state of the art in practical algorithms for scheduling power-systems operations in the short term and the results of the recent competition organized by the U.S. Advanced Research Projects Agency–Energy. We explain the mixed-integer nonlinear formulation used in the competition for nonspecialists in electrical engineering, the context and organization of the competition, and the performance of competitors. We find that the collective approaches and results of competitors provide support for efforts to move nonlinear optimization techniques into industrial applications, as they have proven to be a robust and efficient alternative to current linear approximation techniques.

Studying the effects of Türkiye earthquake disaster and its impact on real estate industry: A risk analysis based on input-output & non-linear optimization models

The real estate industry of Türkiye is highly susceptible to seismic activity. The recent earthquakes have severely impacted the industry and the country's economy. This study examines Türkiye's real estate resilience during earthquakes using the Dynamic Inoperability Input-Output Model (DIIM) and a non-linear optimization technique. According to the findings of DIIM, specific industries, including those dealing with the supply of electricity and gas, chemicals, non-metallic minerals, and financial and insurance intermediaries, suffer significant financial losses. The levels of inoperability are highest in the mining and quarrying industries, followed by the chemical and non-metallic mineral product industries, and then by mining support activities. The top nine most inoperable industries account for approximately $9.5 billion in economic losses, with real estate alone accounting for $27.4 billion. The Fuzzy-FUCOM technique was used to identify significant risk factors related to technological, political, and social hazards, assisting policymakers in making more informed decisions. The novelty of this study is in its application of the DIIM model and a non-linear optimization technique to the challenge of seismic hazard mitigation in Türkiye's real estate market. In conclusion, this study's findings provide insight into Türkiye's affected sectors' risks, recovery time, and adaptability.

Cautious Bayesian MPC: Regret Analysis and Bounds on the Number of Unsafe Learning Episodes

This paper investigates the combination of model predictive control (MPC) concepts and posterior sampling techniques and proposes a simple constraint tightening technique to introduce cautiousness during explorative learning episodes. The provided theoretical analysis in terms of cumulative regret focuses on previously stated sufficient conditions of the resulting ‘Cautious Bayesian MPC’ algorithm and shows Lipschitz continuity of the future reward function in the case of linear MPC problems. In the case of nonlinear MPC problems, it is shown that commonly required assumptions for nonlinear MPC optimization techniques provide sufficient criteria for model-based RL using posterior sampling. Furthermore, it is shown that the proposed constraint tightening implies a bound on the expected number of unsafe learning episodes in the linear and nonlinear case using a soft-constrained MPC formulation. The efficiency of the method is illustrated using numerical examples.