First-order Approach Research Articles

Toward Efficient Modeling of Nonradiative Decay in Extended INVEST: Overcoming Computational Challenges in Quantum Dynamics Simulations.

In recent years, an increasing number of fully organic molecules capable of thermally activated delayed fluorescence (TADF) have been reported, often with very small or even inverted singlet-triplet (INVEST) energy gaps. These molecules typically exhibit complex photophysics due to the close energy levels of multiple singlet and triplet states, which create various transition pathways toward emission. A predictive model for the rates of these transitions is thus essential for assessing the suitability of new materials for light-emitting devices. Quantum Dynamics (QD) calculations are ideal for this purpose, as they include quantum effects, without the limitations of first-order perturbative approaches, also allowing taking into account more than two electronic states at once. However, the huge computational demands of QD methodologies, especially for large molecules, currently limit their use as a standard tool. To address this problem, we here employ a strategy that allows us to include almost the whole set of the vibrational coordinates by selecting the key elements of the Hilbert space that significantly impact dynamics, thereby hugely reducing the computational burden. Application of this protocol to two relatively large INVEST molecules reveals that internal conversion in these systems is very fast, making indirect emissive pathways a possible channel for the population of the S1 state. More importantly, this study demonstrates that the dynamics can be accurately described even with a significantly reduced vibrational space, thus allowing quantum dynamics calculations that yield accurate transition rates in a few minutes of computational time.

First-Order Algorithms for Robust Optimization Problems via Convex-Concave Saddle-Point Lagrangian Reformulation

Robust optimization (RO) is one of the key paradigms for solving optimization problems affected by uncertainty. Two principal approaches for RO, the robust counterpart method and the adversarial approach, potentially lead to excessively large optimization problems. For that reason, first-order approaches, based on online convex optimization, have been proposed as alternatives for the case of large-scale problems. However, existing first-order methods are either stochastic in nature or involve a binary search for the optimal value. We show that this problem can also be solved with deterministic first-order algorithms based on a saddle-point Lagrangian reformulation that avoid both of these issues. Our approach recovers the other approaches’ [Formula: see text] convergence rate in the general case and offers an improved [Formula: see text] rate for problems with constraints that are affine both in the decision and in the uncertainty. Experiment involving robust quadratic optimization demonstrates the numerical benefits of our approach. History: Accepted by Antonio Frangioni, Area Editor for Design & Analysis of Algorithms–Continuous. Funding: This work was supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek [Grant VI.Veni.191E.035] and the Israel Science Foundation [Grant 1460/19]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0200 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0200 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

The Euler-Lagrange equations of nabla derivatives for variational approach to optimization problems on time scales

This paper investigates the variational approach using nabla (denoted as ∇) within the framework of time scales. By employing two different methods, we derive the Euler-Lagrange equations for first-order variational approach to optimization problems involving exponential functions, as well as for those with both exponential functions and their ∇-derivatives. To establish the high-order variational approach to optimization problem, we present the Leibniz Formula for ∇-derivatives along with its proof. Additionally, we determine the high-order variational approach to optimization problem incorporating ∇-derivatives of exponential functions. Through these analyses, we aim to contribute to the understanding and application of the variational calculus on time scales, offering insights into the behavior of dynamic systems governed by exponential functions and their derivatives.

Designing Universally-Approximating Deep Neural Networks: A First-Order Optimization Approach.

Universal approximation capability, also referred to as universality, is an important property of deep neural networks, endowing them with the potency to accurately represent the underlying target function in learning tasks. In practice, the architecture of deep neural networks largely influences the performance of the models. However, most existing methodologies for designing neural architectures, such as the heuristic manual design or neural architecture search, ignore the universal approximation property, thus losing a potential safeguard about the performance. In this paper, we propose a unified framework to design the architectures of deep neural networks with a universality guarantee based on first-order optimization algorithms, where the forward pass is interpreted as the updates of an optimization algorithm. The (explicit or implicit) network is designed by replacing each gradient term in the algorithm with a learnable module similar to a two-layer network or its derivatives. Specifically, we explore the realm of width-bounded neural networks, a common practical scenario, showcasing their universality. Moreover, adding operations of normalization, downsampling, and upsampling does not hurt the universality. To the best of our knowledge, this is the first work that width-bounded networks with universal approximation guarantee can be designed in a principled way. Our framework can inspire a variety of neural architectures including some renowned structures such as ResNet and DenseNet, as well as novel innovations. The experimental results on image classification problems demonstrate that the newly inspired networks are competitive and surpass the baselines of ResNet, DenseNet, as well as the advanced ConvNeXt and ViT, testifying to the effectiveness of our framework.

The localized RBF interpolation with its modifications for solving the incompressible two-phase fluid flows: A conservative Allen–Cahn–Navier–Stokes system

In this research work, we apply a numerical scheme based on the first-order time integration approach combined with the modifications of the meshless approximation for solving the conservative Allen–Cahn–Navier–Stokes equations. More precisely, we first utilize a first-order time discretization for the Navier–Stokes equations and the time-splitting technique of order one for the dynamics of the phase-field variable. Besides, we use the local interpolation based on the Matérn radial function for spatial discretization. We should solve a Poisson equation with the proper boundary conditions to have the divergence-free property during the numerical algorithm. Accordingly, the applied numerical procedure could not give a stable and accurate solution. Instead, we solve a regularization system in a discrete form. To prevent the instability of the numerical solution concerning the convection term, a biharmonic term with a small coefficient based on the high-order hyperviscosity formulation has been added, which has been approximated by a scalable interpolation based on the combination of polyharmonic spline with polynomials (known as the PHS+poly). The obtained full-discrete problem is solved using the biconjugate gradient stabilized method considering a proper preconditioner. We investigate the potency of the numerical scheme by presenting some simulations via uniform, hexagonal, and quasi-uniform nodes on rectangular and irregular domains. Besides, we have compared the proposed meshless method with the standard finite element method due to the used CPU time.

PLS-SEM for Multivariate Analysis: A Practical Guide to Educational Research using SmartPLS

Implementation of PLS-SEM in educational research has developed significantly, but there are variations in the presentation of the analysis results. This study aims to provide practical understanding to researchers who intend to utilize PLS-SEM in multivariate analysis to enhance the recognition and validity of the resultant research outcomes using SmartPLS. This research is a literature study that conducts content analysis of relevant books and publications. The research results present PLS-SEM analysis using SmartPLS on reflective and formative research models with first-order and second-order approaches through measurement model evaluation (outer model) and structural model evaluation (inner model) with various criteria. Evaluation of the reflective measurement model consists of reflective indicator loadings, internal consistency reliability, convergent validity, and discriminant validity. The review of the formative measurement model consists of convergent validity, collinearity, and statistical significance of weights. The structural model evaluation consists of the collinearity test, significance value, f square, R square, Q square, SRMR, PLSpredict, and robustness checks. Therefore, this study can provide guidance using SmartPLS in conducting PLS-SEM analysis and presenting acceptable analysis results.

Hierarchical characterization of thermoelectric performance in copper-based chalcogenide CsCu3S2: Unveiling the role of anharmonic lattice dynamics

Fundamental understanding of anharmonic lattice dynamics and heat conductance physics in crystalline compounds is critical for the development of thermoelectric energy conversion devices. Herein, we thoroughly investigate the microscopic mechanisms of thermal transport in CsCu3S2 by coupling the self-consistent phonon (SCP) theory with the linearized Wigner transport equation (LWTE). We explicitly consider both phonon energy shifts and broadening arising from both cubic and quartic anharmonicities, as well as diagonal/non-diagonal terms of heat flux operators in thermal conductivity. Our findings show that the strong anharmonicity of CsCu3S2 primarily arises from the presence of p-d anti-bonding hybridization between Cu and S atoms, coupled with the random oscillations of Cs atoms. Notably, the competition between phonon hardening described by the loop diagram and softening induced by the bubble diagram significantly influences particle-like propagation, predominantly reflected in group velocity and energy-conservation rule. Additionally, the electrical transport properties are determined by employing the precise momentum relaxation-time approximation (MRTA). At high temperatures, the thermoelectric performance of p-type CsCu3S2 reaches its optimum theoretical value of 0.94 along the in-plane direction based on advanced phonon renormalization theory. In striking contrast, the harmonic approximation theory significantly overestimates the thermoelectric efficiency at the same temperatures, rendering it an impractical expectation. Conversely, the first-order renormalization approach leads to a serious underestimation of the thermoelectric properties due to the over-correction of phonon energy. Our study not only reveals the pivotal role of anharmonic lattice dynamics in accurately assessing thermoelectric properties but also underscores the potential thermoelectric applications for novel copper-based chalcogenides.

Explicit computational analysis of unsteady maxwell nanofluid flow on moving plates with stochastic variations

It is imperative to investigate the proposed computational scheme for the resolution of two-dimensional partial differential equations that result from non-Newtonian nanofluid flow over flat and oscillatory sheets, taking into account the effects of the magnetic field and chemical reactions, as it is designed to address stochasticity, unstable flow conditions, and Maxwellian behaviour. Consequently, it offers valuable insights into the dynamics of nanofluids. A stochastic computational scheme is suggested to address the two-dimensional partial differential equations (PDEs) caused by non-Newtonian nanofluid flow over flat and oscillatory sheets in the presence of a magnetic field and chemical reaction effects. The Taylor series analysis is employed to construct a scheme. The two-stage approach can be employed to discretize the time derivative in the differential equations. The stability study results and the consistency by mean square measure are also included. The continuity equation in the given partial differential equations (PDEs) is discretized using the first-order finite difference approach. The remaining equations, including the energy equation, the nanoparticle volume fraction, and the Navier-Stokes equation, are discretized using the second-order difference in space scheme that is proposed. Three separate figures show how the various parameters affect the nanoparticle volume fractions, velocity, and temperature. Through a focus on a specific computational technique designed to handle the challenges given by stochasticity, unstable flow conditions, and the Maxwellian behaviour shown by these nanofluids, this study introduction serves as a portal into the involved domain of nanofluid dynamics.

Microbiological Risk Assessment of High-Demand Food from Three Major Cities in Ecuador

The current study was carried out to estimate the risk of disease probability from the consumption of foods such as meats, poultry, unpasteurized cheeses, fruit-based drinks, ready-to-eat fruits, and typical preparations such as Encebollado, ceviche, and Bolón de Verde contaminated with Salmonella, Escherichia coli and Listeria monocytogenes in Ecuador using a quantitative microbiological risk assessment (QMRA). A first-order Monte Carlo simulation probabilistic distribution approach was adopted to assess the occurrence of pathogens in the tested foods. 27 The scenario was simulated using the concentration levels concerning the contaminant and food consumption obtained through an online survey with a sample size of 202 people. A model (100,000 iterations) was run and created in an Excel spreadsheet using @Risk software. The results obtained are the risk of infection (possibilities of becoming infected by eating the food evaluated) and the contaminant dose per portion consumed. Additionally, an exponential model with a single dose was used for risk characterization to determine the probability of becoming ill from contaminated food. The QMRA model performed a prediction for the mean risk of Salmonella infection from ground beef consumption of 1.33 E - 04 log 10 cfu / serving, while the exponential model estimated a value of 1.0 log cfu - serving. In the case of Listeria monocytogenes, the QMRA estimated an average probability of infection in unpasteurized fresh cheese of 5.9E-05 compared to the average disease risk estimated in the risk characterization for L. monocytogenes of 9.50E-13. The QMRA estimated an average risk of infection by E. coli for Encebollado and ceviches of 5.6E -03 compared to the average risk of disease estimated in the risk characterization for Escherichia coli of 0.387 log cfu -ration. These results suggest the need to adopt effective mitigation strategies. Control parameters such as temperature during the supply chain and good hygiene practices during manufacturing can effectively control food-associated pathogens. More data is necessary toimprove the evaluation of the risk developed. Keywords: Microbiological risk análisis, Infectious biological agents (Salmonella, Listeria monocytogenes, Escherichia coli), QMRA (Quantitative Microbial Risk Assessment), Typical foods in Ecuador, Population food consumption in three main cities of Ecuador.

Microbiological Risk Assessment of High-Demand Food from Three Major Cities in Ecuador

The current study was carried out to estimate the risk of disease probability from the consumption of foods such as meats, poultry, unpasteurized cheeses, fruit-based drinks, ready-to-eat fruits, and typical preparations such as Encebollado, ceviche, and Bolón de Verde contaminated with Salmonella, Escherichia coli and Listeria monocytogenes in Ecuador using a quantitative microbiological risk assessment (QMRA). A first-order Monte Carlo simulation probabilistic distribution approach was adopted to assess the occurrence of pathogens in the tested foods. The scenario was simulated using the concentration levels concerning the contaminant and food consumption obtained through an online survey with a sample size of 202 people. A model (100,000 iterations) was run and created in an Excel spreadsheet using @Risk software. The results obtained are the risk of infection (possibilities of becoming infected by eating the food evaluated) and the contaminant dose per portion consumed. Additionally, an exponential model with a single dose was used for risk characterization to determine the probability of becoming ill from contaminated food. The QMRA model performed a prediction for the mean risk of Salmonella infection from ground beef consumption of 1.33 E - 04 log 10 cfu / serving, while the exponential model estimated a value of 1.0 log cfu - serving. In the case of Listeria monocytogenes, the QMRA estimated an average probability of infection in unpasteurized fresh cheese of 5.9E-05 compared to the average disease risk estimated in the risk characterization for L. monocytogenes of 9.50E-13. The QMRA estimated an average risk of infection by E. coli for Encebollado and ceviches of 5.6E -03 compared to the average risk of disease estimated in the risk characterization for Escherichia coli of 0.387 log cfu -ration. These results suggest the need to adopt effective mitigation strategies. Control parameters such as temperature during the supply chain and good hygiene practices during manufacturing can effectively control food-associated pathogens. More data is necessary toimprove the evaluation of the risk developed. Keywords: Microbiological risk análisis, Infectious biological agents (Salmonella, Listeria monocytogenes, Escherichia coli), QMRA (Quantitative Microbial Risk Assessment), Typical foods in Ecuador, Population food consumption in three main cities of Ecuador.

Trajectory tracking controller design for wheeled Mobile robot with velocity and torque constraints

This article investigates the trajectory tracking control problem for wheeled mobile robot (WMR) subject to both velocity and torque constraints. Firstly, a more general model is established by considering the displacement between the centre of mass and the midpoint of the driving wheels of the WMR, based on which, a new bounded kinematic controller is proposed by combining the first-order filtering approach to keep the trajectory tracking error asymptotically stable. Then the dynamic controller is designed and the stability of the overall closed-loop system is proved by the Lyapunov stability theory and Barbalat's lemma. Some conditions are given to ensure that both the velocity constraints and torque constraints are satisfied. Finally, some numerical examples are given to show the effectiveness and advantages of the method proposed in this paper.

Integral field spectroscopy supports atmospheric optics to reveal the finite outer scale of the turbulence

The spatial coherence wavefront outer scale ( characterizes the size of the largest turbulence eddies in Earth's atmosphere, determining low spatial frequency perturbations in the wavefront of the light captured by ground-based telescopes. Advances in adaptive optics (AO) techniques designed to compensate for atmospheric turbulence emphasize the crucial role of this parameter for the next generation of large telescopes. The motivation of this work is to introduce a novel technique for estimating \ from seeing-limited integral field spectroscopic (IFS) data. This approach is based on the impact of a finite \ on the light collected by the pupil entrance of a ground-based telescope. We take advantage of the homogeneity of IFS observations to generate band filter images spanning a wide wavelength range, enabling the assessment of image quality (IQ) at the telescope's focal plane. Comparing the measured wavelength-dependent IQ variation with predictions derived from a first-order analytical approach based on turbulence statistics simplifications using the von Kármán model provides valuable insights into the prevailing \ parameter during the observations. We applied the proposed technique to observations from the Multi-Unit Spectroscopic Explorer (MUSE) in the wide-field mode obtained at the Paranal Observatory. Our analysis successfully validates the first-order analytical expression, which combines the seeing ($ $) and the \ parameters, to predict the IQ variations with the wavelength in ground-based astronomical data. However, we observed some discrepancies between the measured and predictions of the IQ that are analyzed in terms of uncertainties in the estimated $ $ and dome-induced turbulence contributions. This work constitutes the empirical validation of the analytical expression for estimating IQ at the focal plane of ground-based telescopes under specific $ $ and finite \ conditions. Additionally, we provide a simple methodology to characterize the \ and dome-seeing ($ dome $) as by-products of IFS observations routinely conducted at major ground-based astronomical observatories.

Linkages between urban growth and land surface temperature variations in the Seoul metropolitan area: A spatial first-order difference approach

This study investigates the effects of urban development and expansion on Land Surface Temperature (LST) changes from 2000 to 2018, using the Seoul Metropolitan area (SMA) as a case study area. Along with descriptive analysis, this study uses a spatial first-order difference model to statistically analyze the longitudinal relationship between land use features and LST, including impervious surface (IS), enhanced vegetation index (EVI), anthropogenic factors, and urban spatial and topographical factors as well as urban development types as influential factors on LST variations. Our findings support prior research indicating the cooling effects of vegetation and warming effects of imperviousness. We also found a positive association between detached housing units, manufacturing activities and LST changes and a negative relationship between apartment units, urban parks, service activities and LST changes. More importantly, substantial LST reduction was found in the large-scale high-rise apartment complexes redeveloped from the low-rise, detached housing sites in inner-city infill areas, contrasting with significant LST rise in the suburban new town development. We suggest redevelopment of inner-city low-rise compact areas into high-rise but greener blocks as a LST mitigation strategy, equipped with cooling strategies such as green infrastructure and climate-sensitive design considering local microclimate and natural ventilation.

Hybrid hydropeaking mitigation at storage hydropower plants combining compensation basins with battery energy storage systems (BESS)

Storage hydropower has the ability of flexibly generating electricity to match fluctuating power demand. However, rapid changes of water discharge in river reaches downstream of storage hydropower plants, referred to as hydropeaking, result from this intermittent production mode and may have potentially damaging effects on a river’s ecosystem. The construction of compensation basins usually embedded along the waterway between the powerhouse and the receiving water represents the state-of-the-art for hydropeaking mitigation. In recent studies, the application of battery energy storage systems (BESS) as an alternative mitigation option has been proposed. Instead of buffering the turbine discharge in a basin, electrical energy is stored in and retrieved from a BESS to meet short-term demand requirements, while the hydraulic machinery is ramping up and down according to environmental discharge constraints. The technical and economic feasibility of BESS compared to compensation basins is evaluated based on a newly introduced first-order assessment approach. If environmental discharge constraints are to be strictly followed, the exclusive application of BESS is deemed not feasible, due to the limited operation range of Francis and – to a lesser extent – Pelton turbines, especially for low partial loads. Therefore, hybrid systems combining a BESS with a smaller compensation basin are investigated as existing research focused either on a basin- or a BESS-only approach. Based on production time series of three case study hydropower plants, the sizes of basins and BESS are estimated. Basin sizes can be reduced with a hybrid system by 51% to 96% compared to a basin-only approach, with BESS energy capacities ranging approximately from 10 to 100 MWh. The cost efficiency of hybrid systems is strongly influenced by two factors, namely the future battery costs as well as the overall unit costs for the compensating basin. While the former are subject to considerable uncertainty especially as BESS reach their end-of-life much earlier compared to hydraulic structures and therefore require regular replacements after 10 to 15 years, the latter are highly site-specific as they include land availability and acquisition costs. The case studies show that a hybrid system of basin and BESS may represent a cost-competitive alternative to a basin-only approach when the latter’s investment costs are high or space is limited, even if additional revenue streams including ancillary services and energy arbitrage are not considered.

Using Ant Colony Optimization to Identify Optimal Sample Allocations in Cluster-Randomized Trials

When designing cluster-randomized trials (CRTs), one important consideration is determining the proper sample sizes across levels and treatment conditions to cost-efficiently achieve adequate statistical power. This consideration is usually addressed in an optimal design framework by leveraging the cost structures of sampling and optimizing the sampling ratios across treatment conditions and levels of the hierarchy. Traditionally, optimization is done through the first-order derivative approach by setting the first-order derivatives equal to zero to solve for the optimal design parameters. However, the first-order derivative method is incapable of properly handling the optimization task when statistical power formulas are complex, such as those for CRTs detecting mediation effects under the joint significance test. The current study proposes using an ant colony optimization (ACO) algorithm to identify optimal allocations. We evaluate the algorithm’s performance for CRTs detecting main and mediation effects. The results show that the ACO algorithm can identify optimal sample allocations for CRTs investigating main effects with the same design efficiency as those identified through the first-order derivative method. Furthermore, it can efficiently identify optimal sample allocations for CRTs investigating mediation effects under the joint significance test. We have implemented the proposed methods in the R package odr.

The SUSY partners of the QES sextic potential revisited

In this paper, the SUSY partner Hamiltonians of the quasi-exactly solvable (QES) sextic potential Vqes(x)=νx6+2νμx4+μ2−(4N+3)νx2 , N∈Z+ , are revisited from a Lie algebraic perspective. It is demonstrated that, in the variable z = x 2, the underlying sl2(R) hidden algebra of V qes(x) is inherited by its SUSY partner potential V 1(x) only for N = 0. At fixed N > 0, the algebraic polynomial operator h(x, ∂ x ; N) that governs the N exact eigenpolynomial solutions of V 1 is derived explicitly. These odd-parity solutions appear in the form of zero modes. The potential V 1 can be represented as the sum of a polynomial and rational parts. In particular, it is shown that the polynomial component is given by V qes with a different non-integer (cohomology) parameter N1=N−32 . A confluent second-order SUSY transformation is also implemented for a modified QES sextic potential possessing the energy reflection symmetry. By taking N as a continuous real constant and using the Lagrange-mesh method, highly accurate values (∼20 s. d.) of the energy E n = E n (N) in the interval N ∈ [ − 1, 3] are calculated for the three lowest states n = 0, 1, 2 of the system. The critical value N c above which tunneling effects (instanton-like terms) can occur is obtained as well. At N = 0, the non-algebraic sector of the spectrum of V qes is described by means of compact physically relevant trial functions. These solutions allow us to determine the effects in accuracy when the first-order SUSY approach is applied on the level of approximate eigenfunctions.

Revisiting the First-Order Approach to Principal-Agent Problems

Revisiting the First-Order Approach to Principal-Agent Problems

Numerical computation of quasinormal modes in the first-order approach to black hole perturbations in modified gravity

We present a novel approach to the numerical computation of quasi-normal modes, based on the first-order (in radial derivative) formulation of the equations of motion and using a matrix version of the continued fraction method. This numerical method is particularly suited to the study of static black holes in modified gravity, where the traditional second-order, Schrödinger-like, form of the equations of motion is not always available. Our approach relies on the knowledge of the asymptotic behaviours of the perturbations near the black hole horizon and at spatial infinity, which can be obtained via the systematic algorithm that we have proposed recently. In this work, we first present our method for the perturbations of a Schwarzschild black hole and show that we recover the well-know frequencies of the QNMs to a very high precision. We then apply our method to the axial perturbations of an exact black hole solution in a particular scalar-tensor theory of gravity. We also cross-check the obtained QNM frequencies with other numerical methods.

Groundwater Responses of Foundation Subjected to Water Level Fluctuation of Reservoir Considering Variability of Layered Structure

The effect of the variability in a layered structure, characterized by the spatial variability of the saturated hydraulic conductivity, on the distribution of a pressure head p in a foundation subjected to water level fluctuation in a reservoir is investigated with the aid of the random field theory, Karhunen–Loève (K-L) expansion, first-order moment approach, and cross-correlation analysis. The results show that the variability in the foundation structure has significant impacts on the groundwater response to the reservoir’s water level fluctuations. Regions with relatively large uncertainties of the p and σp values in the foundation are those around the initial water level at the reservoir side, and those at the distal end away from the reservoir. In addition, there is a larger variance of Ks, denoted as σlnKs2, a larger correlation scale in the horizontal direction λh, a larger correlation scale in the vertical direction λv, and a larger one-way time consumption of fluctuations T to a larger uncertainty in p. Moreover, the four factors (σlnKs2, λh, λv, and T) all have positive correlations with σp. σlnKs2 has the largest impact on σp in the foundation, λv has the second largest impact, and λh has the smallest impact. A foundation with small Ks values around the initial water level at the reservoir side and large Ks values around the highest water level at the reservoir side may produce larger p values in the foundation. These results yield useful insight into the effect of the variability in a layered structure on the distribution of the pressure head in a foundation subjected to water level fluctuation in a reservoir.

A Quasi-Newton Matrix Factorization-Based Model for Recommendation

Solving large-scale non-convex optimization problems is the fundamental challenge in the development of matrix factorization (MF)-based recommender systems. Unfortunately, employing conventional first-order optimization approaches proves to be an arduous endeavor since their curves are very complex. The exploration of second-order optimization methods holds great promise. They are more powerful because they consider the curvature of the optimization problem, which is captured by the second-order derivatives of the objective function. However, a significant obstacle arises when directly applying Hessian-based approaches: their computational demands are often prohibitively high. Therefore, the authors propose AdaGO, a novel quasi-Newton method-based optimizer to meet the specific requirements of large-scale non-convex optimization problems. AdaGO can strike a balance between computational efficiency and optimization performance. In the comparative studies with state-of-the-art MF-based models, AdaGO demonstrates its superiority by achieving higher prediction accuracy.