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Journal articles on the topic 'Trust Region Model'

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Author: Grafiati

Published: 10 December 2022

Last updated: 29 January 2023

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1

Rodrı́guez, José F., John E. Renaud, Brett A. Wujek, and Ravindra V. Tappeta. "Trust region model management in multidisciplinary design optimization." Journal of Computational and Applied Mathematics 124, no. 1-2 (December 2000): 139–54. http://dx.doi.org/10.1016/s0377-0427(00)00424-6.

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2

Wu, Shwu-Ing. "Competing Model of Event Marketing Activities." International Journal of Marketing Studies 8, no. 4 (July 27, 2016): 52. http://dx.doi.org/10.5539/ijms.v8n4p52.

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<p>Event marketing is the important strategy for the regional tourism development. It is worthwhile to be discussed that the cooperation between regional image and physical environment can shape the regional features and intensify tourists’ attitudes and tourist willingness towards regions. This study took the regular event marketing activities (Xinshe Sea of Flowers events in Taichung; Sakura Festival in Formosa Aboriginal Culture Village in Sun Moon Lake) held in two regions in Taiwan as the examples to discuss the effect of event marketing activities in different regions, regional image and physical environment on tourists’ experiential value, satisfaction, trust and commitment, so as to establish the competing model, compare the intensity difference in each path relationship and deeply analyze the effect of different event marketing activities.</p><p>After the analysis of 500 valid questionnaires, it can be found that: (1) the event marketing activities and physical environment in two regions both have the significantly positive effect on tourists’ experiential value; (2) The tourists’ experiential value has the significantly positive effect on satisfaction and trust; (3) The tourists’ trust has the significantly positive effect on commitment; (4) However, the regional image has no significant effect on tourists’ experiential value. Besides, there is significant difference in the influencing intensity of the two paths: (1) The tourists’ satisfaction for Xinshe Sea of Flowers events in Taichung has the significantly positive effect on trust, while there is no significantly positive effect in the other region; (2) The influencing intensity of tourists’ experiential value for Sakura Festival in Formosa Aboriginal Culture Village in Sun Moon Lake on trust is significantly greater than that in the other region. It can be seen that the event marketing in different regions can generate the impact with different intensity. Therefore, each region should cooperate with its physical environment to plan the characteristic event marketing strategies.<strong></strong></p>

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3

McCartin, Brian J. "A model-trust region algorithm utilizing a quadratic interpolant." Journal of Computational and Applied Mathematics 91, no. 2 (May 1998): 249–59. http://dx.doi.org/10.1016/s0377-0427(98)00052-1.

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4

Cui, Zhaocheng. "A Nonmonotone Adaptive Trust Region Method Based on Conic Model for Unconstrained Optimization." Journal of Optimization 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/237279.

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We propose a nonmonotone adaptive trust region method for unconstrained optimization problems which combines a conic model and a new update rule for adjusting the trust region radius. Unlike the traditional adaptive trust region methods, the subproblem of the new method is the conic minimization subproblem. Moreover, at each iteration, we use the last and the current iterative information to define a suitable initial trust region radius. The global and superlinear convergence properties of the proposed method are established under reasonable conditions. Numerical results show that the new method is efficient and attractive for unconstrained optimization problems.

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5

Zhang, Xin, Jie Wen, and Qin Ni. "Subspace trust-region algorithm with conic model for unconstrained optimization." Numerical Algebra, Control & Optimization 3, no. 2 (2013): 223–34. http://dx.doi.org/10.3934/naco.2013.3.223.

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6

Dæhlen, Jon S., Gisle Otto Eikrem, and Tor Arne Johansen. "Nonlinear model predictive control using trust-region derivative-free optimization." Journal of Process Control 24, no. 7 (July 2014): 1106–20. http://dx.doi.org/10.1016/j.jprocont.2014.04.011.

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7

Ni, Qin. "Optimality Conditions for Trust-Region Subproblems Involving a Conic Model." SIAM Journal on Optimization 15, no. 3 (January 2005): 826–37. http://dx.doi.org/10.1137/s1052623402418991.

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8

Zhu, Honglan, Qin Ni, Liwei Zhang, and Weiwei Yang. "A Fractional Trust Region Method for Linear Equality Constrained Optimization." Discrete Dynamics in Nature and Society 2016 (2016): 1–10. http://dx.doi.org/10.1155/2016/8676709.

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A quasi-Newton trust region method with a new fractional model for linearly constrained optimization problems is proposed. We delete linear equality constraints by using null space technique. The fractional trust region subproblem is solved by a simple dogleg method. The global convergence of the proposed algorithm is established and proved. Numerical results for test problems show the efficiency of the trust region method with new fractional model. These results give the base of further research on nonlinear optimization.

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9

Kartika, Chandra, Chamariyah Chamariyah, Rena Febrita Sarie, and Veronika Nugraheni Sri Lestari. "Model Radical Marketing and Customer Satisfaction Bank Jatim Branch Sememi Surabaya Region." IJEBD (International Journal of Entrepreneurship and Business Development) 5, no. 5 (September 30, 2022): 965–70. http://dx.doi.org/10.29138/ijebd.v5i5.1993.

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Purpose: The purpose of the study is to test and analyze the Influence of Service Marketing, Referral Marketing, Trust Icon Corporate on Radical Marketing through Customer Satisfaction at Bank Jatim Sememi Branch Surabaya. Design/methodology/approach: Purposive Sampling Method. The total sample of 100 Customer Respondents at Bank Jatim Sememi Branch. This research is a Survey Research and Quantitative approach. The data analysis technique of this study uses the Partial Least Square (PLS) method. Findings: The results of Service Marketing Research do not directly affect Customer Satisfaction, Referral Marketing has a direct effect on Customer Satisfaction, Trust Icon Corporate does not directly affect Customer Satisfaction, Service Marketing has a direct effect on Radical Marketing, Referral Marketing has a direct effect on Radical Marketing, Trust Icon Corporate directly affects Radical Marketing. Service Marketing does not have an indirect effect on Radical Marketing through Customer Satisfaction. Radical Marketing does not have an indirect effect on Radical Marketing through Customer Satisfaction. Trust Icon Corporate does not indirectly affect Radical Marketing through Customer Satisfaction. Originality/value: This paper is original Paper type: Research paper

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10

Pérez-Archila, Luis Miguel, Juan David Bastidas Rodriguez, and Rodrigo Correa1. "Solución del modelo de un generador fotovoltaico utilizando los algoritmos de optimización Trust Region Dogleg y PSO." Revista UIS Ingenierías 19, no. 1 (January 1, 2020): 37–48. http://dx.doi.org/10.18273/revuin.v19n1-2020003.

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El modelo matemático de un generador fotovoltaico en conexión Serie-Paralelo representado mediante el modelo de diodo simple, tiene asociado a él un sistema de ecuaciones no lineales. En este trabajo se propone la solución de estos sistemas empleando los métodos de optimización Trust Region Dogleg y Optimización por Enjambre de Partículas, para resolver el modelo de un generador fotovoltaico operando en condiciones homogéneas y no homogéneas, variando el número de submódulos y el patrón de sombreado que incide sobre el generador. Se realizó la simulación de los modelos para generadores compuestos por 3 y 15 submódulos en serie, bajo diferentes condiciones de sombreado. De los métodos implementados, Trust Region Doglegmostró un mejor desempeño con tiempos de cómputo 2 y 14 veces menores que el método de referencia y Optimización por Enjambre de Partículas, respectivamente. Y un error medio cuadrático igual o un 50% inferior a los otros métodos

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11

Wang, JianYu, and Qin Ni. "An algorithm for solving new trust region subproblem with conic model." Science in China Series A: Mathematics 51, no. 3 (March 2008): 461–73. http://dx.doi.org/10.1007/s11425-007-0149-6.

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12

Qu, Shao-Jian, Ke-Cun Zhang, and Jian Zhang. "A nonmonotone trust-region method of conic model for unconstrained optimization." Journal of Computational and Applied Mathematics 220, no. 1-2 (October 2008): 119–28. http://dx.doi.org/10.1016/j.cam.2007.07.038.

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13

Di, Simon, and Wenyu Sun. "A trust region method for conic model to solve unconstraind optimizaions∗." Optimization Methods and Software 6, no. 4 (January 1996): 237–63. http://dx.doi.org/10.1080/10556789608805637.

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14

Qu, Shao-Jian, and Su-Da Jiang. "A trust-region method with a conic model for unconstrained optimization." Mathematical Methods in the Applied Sciences 31, no. 15 (October 2008): 1780–808. http://dx.doi.org/10.1002/mma.997.

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15

Li, Ningning, Dan Xue, Wenyu Sun, and Jing Wang. "A Stochastic Trust Region Method for Unconstrained Optimization Problems." Mathematical Problems in Engineering 2019 (February 3, 2019): 1–10. http://dx.doi.org/10.1155/2019/8095054.

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In this paper, a stochastic trust region method is proposed to solve unconstrained minimization problems with stochastic objectives. Particularly, this method can be used to deal with nonconvex problems. At each iteration, we construct a quadratic model of the objective function. In the model, stochastic gradient is used to take the place of deterministic gradient for both the determination of descent directions and the approximation of the Hessians of the objective function. The behavior and the convergence properties of the proposed method are discussed under some reasonable conditions. Some preliminary numerical results show that our method is potentially efficient.

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16

Keil, Tim, Luca Mechelli, Mario Ohlberger, Felix Schindler, and Stefan Volkwein. "A non-conforming dual approach for adaptive Trust-Region reduced basis approximation of PDE-constrained parameter optimization." ESAIM: Mathematical Modelling and Numerical Analysis 55, no. 3 (May 2021): 1239–69. http://dx.doi.org/10.1051/m2an/2021019.

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In this contribution we propose and rigorously analyze new variants of adaptive Trust-Region methods for parameter optimization with PDE constraints and bilateral parameter constraints. The approach employs successively enriched Reduced Basis surrogate models that are constructed during the outer optimization loop and used as model function for the Trust-Region method. Each Trust-Region sub-problem is solved with the projected BFGS method. Moreover, we propose a non-conforming dual (NCD) approach to improve the standard RB approximation of the optimality system. Rigorous improved a posteriori error bounds are derived and used to prove convergence of the resulting NCD-corrected adaptive Trust-Region Reduced Basis algorithm. Numerical experiments demonstrate that this approach enables to reduce the computational demand for large scale or multi-scale PDE constrained optimization problems significantly.

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17

Lidberg, Johan, and David Robie. "EDITORIAL: Trust and transparency." Pacific Journalism Review 18, no. 2 (October 31, 2012): 6. http://dx.doi.org/10.24135/pjr.v18i2.258.

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Since the call for papers to the theme for this issue of the Pacific Journalism Review, more tumultuous events in journalism have unfolded dominated by the agonising restructure of the newspaper arms of media companies across the region. Hundreds of editorial jobs are on the line. The increasingly desperate search for the ‘new business model’ has been stepped up. But is the new model the only answer to the current plight of journalism? Are media proprietors paying enough attention to the fact that the business model is built on the public trusting the journalistic practices that sit at the heart of the media brands? Perhaps all stakeholders should pay closer attention to Conboy’s thoughts?

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18

Zhang, Shu E., Xue Wang, and Kai Wang. "Study of Optimization of Microwave Cavity Filter Parameters Based on a Hybrid Algorithm of Trust Region." Applied Mechanics and Materials 713-715 (January 2015): 1180–83. http://dx.doi.org/10.4028/www.scientific.net/amm.713-715.1180.

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Optimization of microwave filter structure parameter based on traditional learning methods faces problems like long design cycles, complex calculation and sensitive to initial value, and so on. A hybrid trust region algorithm which combine the improved trust region with the advance and retreat method is introduced to the field of optimization of microwave filter structure parameter for the first time. Comparison between the methods based on the traditional trust region method and the improved trust region method reveals that the algorithm can significantly increase precision and speed of optimization model of the microwave cavity filter parameters.

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19

Fröhlich, Fabian, and Peter K. Sorger. "Fides: Reliable trust-region optimization for parameter estimation of ordinary differential equation models." PLOS Computational Biology 18, no. 7 (July 13, 2022): e1010322. http://dx.doi.org/10.1371/journal.pcbi.1010322.

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Ordinary differential equation (ODE) models are widely used to study biochemical reactions in cellular networks since they effectively describe the temporal evolution of these networks using mass action kinetics. The parameters of these models are rarely known a priori and must instead be estimated by calibration using experimental data. Optimization-based calibration of ODE models on is often challenging, even for low-dimensional problems. Multiple hypotheses have been advanced to explain why biochemical model calibration is challenging, including non-identifiability of model parameters, but there are few comprehensive studies that test these hypotheses, likely because tools for performing such studies are also lacking. Nonetheless, reliable model calibration is essential for uncertainty analysis, model comparison, and biological interpretation. We implemented an established trust-region method as a modular Python framework (fides) to enable systematic comparison of different approaches to ODE model calibration involving a variety of Hessian approximation schemes. We evaluated fides on a recently developed corpus of biologically realistic benchmark problems for which real experimental data are available. Unexpectedly, we observed high variability in optimizer performance among different implementations of the same mathematical instructions (algorithms). Analysis of possible sources of poor optimizer performance identified limitations in the widely used Gauss-Newton, BFGS and SR1 Hessian approximation schemes. We addressed these drawbacks with a novel hybrid Hessian approximation scheme that enhances optimizer performance and outperforms existing hybrid approaches. When applied to the corpus of test models, we found that fides was on average more reliable and efficient than existing methods using a variety of criteria. We expect fides to be broadly useful for ODE constrained optimization problems in biochemical models and to be a foundation for future methods development.

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20

Zhu, Honglan, Qin Ni, and Meilan Zeng. "A quasi-Newton trust region method based on a new fractional model." Numerical Algebra, Control & Optimization 5, no. 3 (2015): 237–49. http://dx.doi.org/10.3934/naco.2015.5.237.

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21

Abdel-Malek, Hany L., Shaimaa E. K. Ebid, and Ahmed S. A. Mohamed. "A trust region approach with multivariate Padé model for optimal circuit design." Engineering Optimization 49, no. 11 (February 15, 2017): 1978–94. http://dx.doi.org/10.1080/0305215x.2017.1282728.

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22

XU, Dong, and WenYu SUN. "A filter-trust-region method based on conic model for unconstrained optimization." SCIENTIA SINICA Mathematica 42, no. 5 (May 1, 2012): 527–43. http://dx.doi.org/10.1360/012012-137.

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23

Yi, Cunxiao, and Lei Wang. "A Non-Monotone Trust Region Algorithm with Memory Model for Unconstrained Optimization." Information Technology Journal 10, no. 9 (August 15, 2011): 1847–49. http://dx.doi.org/10.3923/itj.2011.1847.1849.

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24

Honglan, Zhu, Ni Qin, Dang Changyin, and Zhang Hao. "A trust region method based on the fractional model for unconstrained optimization." SCIENTIA SINICA Mathematica 48, no. 4 (March 19, 2018): 531. http://dx.doi.org/10.1360/scm-2016-0115.

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25

Chengjing, Wang. "A trust region method with a conic model for nonlinearly constrained optimization." Applied Mathematics-A Journal of Chinese Universities 21, no. 3 (September 2006): 263–75. http://dx.doi.org/10.1007/s11766-003-0003-8.

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26

Yu, Wangxun, and Aiju Wang. "New Solutions of Nonlinear Equations Constrained by Bounded Variables under Edge Computation." Wireless Communications and Mobile Computing 2022 (May 28, 2022): 1–11. http://dx.doi.org/10.1155/2022/9855672.

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Aiming at the problem of low global convergence and local convergence rate of trust region interior points of bounded variable constrained nonlinear equations, a trust region interior point algorithm for bounded variable constrained nonlinear equations under edge calculation is designed. By constructing the basic function form of nonlinear equations constrained by bounded variables, the boundary of nonlinear equations is determined by Gauss Newton iterative process to ensure the global convergence of changes; solve the original objective function, analyze the trust region subproblem of the unconstrained optimization problem, and generate an acceptable region. The region is generated through two-dimensional example interpretation. The interior points in the acceptable region are determined by the primal dual interior point method, and the interior points in the acceptable region are optimized. With the help of edge calculation, the trust region interior point programming model of bounded variable constrained nonlinear equations is designed to realize the algorithm design. The experimental results show that the designed algorithm can improve the trust region interior point global convergence and local convergence rate of nonlinear equations with bounded variable constraints.

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27

Zhao, Lijuan. "Nonmonotone conic trust region method with line search technique for bound constrained optimization." RAIRO - Operations Research 53, no. 3 (June 24, 2019): 787–805. http://dx.doi.org/10.1051/ro/2017054.

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In this paper, we propose a nonmonotone trust region method for bound constrained optimization problems, where the bounds are dealt with by affine scaling technique. Differing from the traditional trust region methods, the subproblem in our algorithm is based on a conic model. Moreover, when the trial point isn’t acceptable by the usual trust region criterion, a line search technique is used to find an acceptable point. This procedure avoids resolving the trust region subproblem, which may reduce the total computational cost. The global convergence and Q-superlinear convergence of the algorithm are established under some mild conditions. Numerical results on a series of standard test problems are reported to show the effectiveness of the new method.

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28

March, A., K. Willcox, and Q. Wang. "Gradient-based multifidelity optimisation for aircraft design using Bayesian model calibration." Aeronautical Journal 115, no. 1174 (December 2011): 729–38. http://dx.doi.org/10.1017/s0001924000006473.

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Abstract Optimisation of complex systems frequently requires evaluating a computationally expensive high-fidelity function to estimate a system metric of interest. Although design sensitivities may be available through either direct or adjoint methods, the use of formal optimisation methods may remain too costly. Incorporating low-fidelity performance estimates can substantially reduce the cost of the high-fidelity optimisation. In this paper we present a provably convergent multifidelity optimisation method that uses Cokriging Bayesian model calibration and first-order consistent trust regions. The technique is compared with a single-fidelity sequential quadratic programming method and a conventional first-order trust-region method on both a two-dimensional structural optimisation and an aerofoil design problem. In both problems adjoint formulations are used to provide inexpensive sensitivity information.

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29

Silva, Thiago L., Mathias C. Bellout, Caio Giuliani, Eduardo Camponogara, and Alexey Pavlov. "Derivative-free trust region optimization for robust well control under geological uncertainty." Computational Geosciences 26, no. 2 (February 15, 2022): 329–49. http://dx.doi.org/10.1007/s10596-022-10132-y.

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AbstractA Derivative-Free Trust-Region (DFTR) algorithm is proposed to solve the robust well control optimization problem under geological uncertainty. Derivative-Free (DF) methods are often a practical alternative when gradients are not available or are unreliable due to cost function discontinuities, e.g., caused by enforcement of simulation-based constraints. However, the effectiveness of DF methods for solving realistic cases is heavily dependent on an efficient sampling strategy since cost function calculations often involve time-consuming reservoir simulations. The DFTR algorithm samples the cost function space around an incumbent solution and builds a quadratic polynomial model, valid within a bounded region (the trust-region). A minimization of the quadratic model guides the method in its search for descent. Because of the curvature information provided by the model-based routine, the trust-region approach is able to conduct a more efficient search compared to other sampling methods, e.g., direct-search approaches. DFTR is implemented within FieldOpt, an open-source framework for field development optimization, and is tested in the Olympus benchmark against two other types of methods commonly applied to production optimization: a direct-search (Asynchronous Parallel Pattern Search) and a population-based (Particle Swarm Optimization). Current results show that DFTR has improved performance compared to the model-free approaches. In particular, the method presented improved convergence, being capable to reach solutions with higher NPV requiring comparatively fewer iterations. This feature can be particularly attractive for practitioners who seek ways to improve production strategies while using an ensemble of full-fledged models, where good convergence properties are even more relevant.

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30

Rodri´guez, J. F., J. E. Renaud, and L. T. Watson. "Trust Region Augmented Lagrangian Methods for Sequential Response Surface Approximation and Optimization." Journal of Mechanical Design 120, no. 1 (March 1, 1998): 58–66. http://dx.doi.org/10.1115/1.2826677.

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A common engineering practice is the use of approximation models in place of expensive computer simulations to drive a multidisciplinary design process based on nonlinear programming techniques. The use of approximation strategies is designed to reduce the number of detailed, costly computer simulations required during optimization while maintaining the pertinent features of the design problem. To date the primary focus of most approximate optimization strategies is that application of the method should lead to improved designs. This is a laudable attribute and certainly relevant for practicing designers. However to date few researchers have focused on the development of approximate optimization strategies that are assured of converging to a solution of the original problem. Recent works based on trust region model management strategies have shown promise in managing convergence in unconstrained approximate minimization. In this research we extend these well established notions from the literature on trust-region methods to manage the convergence of the more general approximate optimization problem where equality, inequality and variable bound constraints are present. The primary concern addressed in this study is how to manage the interaction between the optimization and the fidelity of the approximation models to ensure that the process converges to a solution of the original constrained design problem. Using a trust-region model management strategy, coupled with an augmented Lagrangian approach for constrained approximate optimization, one can show that the optimization process converges to a solution of the original problem. In this research an approximate optimization strategy is developed in which a cumulative response surface approximation of the augmented Lagrangian is sequentially optimized subject to a trust region constraint. Results for several test problems are presented in which convergence to a Karush-Kuhn-Tucker (KKT) point is observed.

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31

Hu, Chang Lin, Li Yuan Ma, Yong Jun Li, and Hui Li. "Modal Parameter Simulation and Model Updating for some Launch Platform." Advanced Materials Research 490-495 (March 2012): 1009–13. http://dx.doi.org/10.4028/www.scientific.net/amr.490-495.1009.

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The frequencies and vibration modes of a launch platform are acquired through finite element simulation, and their actual values are obtained through modal test. On this basis, constructing objective function for the structure modal parameter relative residual error to be minimum, can transform model updating problem into optimization problem. Then the trust region algorithm is adopted to solve this optimization problem. This algorithm bears better robustness and computing efficiency. Through model updating, the frequency and vibration mode errors are reduced, supplying a basis for further simulation.

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32

Gaspar, B., A. P. Teixeira, and C. Guedes Soares. "Adaptive surrogate model with active refinement combining Kriging and a trust region method." Reliability Engineering & System Safety 165 (September 2017): 277–91. http://dx.doi.org/10.1016/j.ress.2017.03.035.

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33

Ji, Ying, Yijun Li, Kecun Zhang, and Xinli Zhang. "A new nonmonotone trust-region method of conic model for solving unconstrained optimization." Journal of Computational and Applied Mathematics 233, no. 8 (February 2010): 1746–54. http://dx.doi.org/10.1016/j.cam.2009.09.011.

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34

Cui, Zengru, Gonglin Yuan, Zhou Sheng, Wenjie Liu, Xiaoliang Wang, and Xiabin Duan. "A Modified BFGS Formula Using a Trust Region Model for Nonsmooth Convex Minimizations." PLOS ONE 10, no. 10 (October 26, 2015): e0140606. http://dx.doi.org/10.1371/journal.pone.0140606.

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35

Qu, Shao-Jian, Qing-Pu Zhang, and Su-Da Jiang. "A nonmonotone quasi-Newton trust-region method of conic model for unconstrained optimization." Optimization Methods and Software 24, no. 3 (June 2009): 339–67. http://dx.doi.org/10.1080/10556780902789290.

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36

Zhao, Lijuan, Wenyu Sun, and Raimundo J. B. de Sampaio. "Nonmonotone adaptive trust region method based on simple conic model for unconstrained optimization." Frontiers of Mathematics in China 9, no. 5 (April 21, 2014): 1211–38. http://dx.doi.org/10.1007/s11464-014-0356-8.

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37

Wang, Kexin, Cheng Yang, Zhijiang Shao, Xiaojin Huang, and Lorenz T. Biegler. "A Trust-Region Framework for Real-Time Optimization with Structural Process-Model Mismatch." Vietnam Journal of Mathematics 48, no. 4 (October 13, 2020): 809–30. http://dx.doi.org/10.1007/s10013-020-00442-y.

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38

Pulkkinen, Seppo, Marko M. Mäkelä, and Napsu Karmitsa. "A generative model and a generalized trust region Newton method for noise reduction." Computational Optimization and Applications 57, no. 1 (July 10, 2013): 129–65. http://dx.doi.org/10.1007/s10589-013-9581-4.

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39

Zhang, Jian, Kecun Zhang, and Shaojian Qu. "A nonmonotone adaptive trust region method for unconstrained optimization based on conic model." Applied Mathematics and Computation 217, no. 8 (December 2010): 4265–73. http://dx.doi.org/10.1016/j.amc.2010.10.043.

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40

Zhu, Honglan, and Qin Ni. "A Simple Alternating Direction Method for the Conic Trust Region Subproblem." Mathematical Problems in Engineering 2018 (December 18, 2018): 1–9. http://dx.doi.org/10.1155/2018/5358191.

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A simple alternating direction method is used to solve the conic trust region subproblem of unconstrained optimization. By use of the new method, the subproblem is solved by two steps in a descent direction and its orthogonal direction, the original conic trust domain subproblem into a one-dimensional subproblem and a low-dimensional quadratic model subproblem, both of which are very easy to solve. Then the global convergence of the method under some reasonable conditions is established. Numerical experiment shows that the new method seems simple and effective.

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41

Lefebvre, Tom, Frederik De Belie, and Guillaume Crevecoeur. "A Radial Basis Function-Based Optimization Algorithm with Regular Simplex Set Geometry in Ellipsoidal Trust-Regions." Mathematical Problems in Engineering 2022 (March 2, 2022): 1–21. http://dx.doi.org/10.1155/2022/8362294.

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In this paper, we investigate two ideas in the context of the interpolation-based optimization paradigm tailored to derivative-free black-box optimization problems. The proposed architecture maintains a radial basis function interpolation model of the actual objective that is managed according to a trust-region globalization scheme. We focus on two distinctive ideas. Firstly, we explore an original sampling strategy to adapt the interpolation set to the new trust region. A better-than-linear interpolation model is guaranteed by maintaining a well-poised supporting subset that pursues a near regular simplex geometry of n + 1 points plus the trust-region center. This strategy improves the geometric distribution of the interpolation points whilst also optimally exploiting the existing interpolation set. On account of the associated minimal interpolation set size, the better-than-linear interpolation model will exhibit curvature, which is a necessary condition for the second idea. Therefore, we explore the generalization of the classic spherical to an ellipsoidal trust-region geometry by matching the contour ellipses with the inverse of the local problem hessian. This strategy is enabled by the certainty of a curved interpolation model and is introduced to accounts for the local output anisotropy of the objective function when generating new interpolation points. Instead of adapting the sampling strategy to an ellipsoid, we carry out the sampling in an affine transformed space. The combination of both methods is validated on a set of multivariate benchmark problems and compared with ORBIT.

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42

Jabłoński and Jabłoński. "Trust as a Key Factor in Shaping the Social Business Model of Water Supply Companies." Sustainability 11, no. 20 (October 18, 2019): 5805. http://dx.doi.org/10.3390/su11205805.

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The current principles of doing business differ radically from those that were applied a few years ago. Global economic crises have shown that business must have a more social character. This gave rise to the creation of management solutions that would guarantee the satisfaction of a wide range of corporate stakeholders. In this context, ideas based on social potential began to emerge. As a consequence, the concept of social business models was born, accompanied by an attempt to search for the best business models possible in order to build the appropriate configuration of their components. According to the authors, an attribute of trust may be such a component based on which effective social business models can be built. As water supply companies are social enterprises, they have become the object of scientific research in this case. The purpose of the article is to determine the position of trust in the construction and application of social business models of water supply companies. The scope of the article includes scientific research into water supply companies in the most industrial region of Poland, Upper Silesia, with the most extensive and dense water supply network in the country. In this article, the AHP (analytic hierarchy process) method was used to conduct research. The aim of the analysis was focusing on the issue of trust as a key factor in shaping the social business model of the company. In the questionnaires, respondents were asked to answer questions on the following issues: trust-based organizational behavior at the company; trust-based social capital at the company; trust-based relationships at the company; trust-based processes and activities at the company; trust-based risk at the company; and the trust-based business model at the company. The adopted logic of the scientific argument conducted indicates that trust and its place and role in the social business model of a water supply company have a significant impact on the social and economic performance of the water supply company, and as a consequence, on increased social responsibility towards stakeholders as well. Trust even stabilizes the organization and its business model; it is also a value catalyst and neutralizes the potentially negative impact of the organization on other entities gathered around it. Trust as a stabilizer can also affect the consistency and scalability of the social business model of a water supply company.

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43

Kosolapova, Nataliya A., Anastasia Y. Nikitaeva, and Maria M. Golovacheva. "Openness of Authorities and Trust in The Region: Assessment Tools Based on Social Mining." Journal of Economic Regulation 13, no. 4 (December 30, 2022): 065–74. http://dx.doi.org/10.17835/2078-5429.2022.13.4.065-074.

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The study attempts to use scientometric analysis methods, social mining tools, and econometric modeling to show the relationship between the level of trust in regional economic systems and the openness of authorities. At the same time, trust is considered a risk factor in the development of economic systems due to the significant influence of this informal institution on the activities of economic entities with decision-making. The scientometric analysis of publications on the topic of the work made it possible to establish an exponential increase in the number of scientific articles on trust, openness, social networks, and the corresponding analytical tools. The constructed network maps of keywords made it possible to identify the largest thematic clusters reflecting the concentration of scientific works in research areas, firstly, related to data, algorithms, and technologies for their analysis, network users, and secondly, reflecting various aspects of organizational and individual behavior and what this behavior determines. The quantitative substantiation of the relationship between the openness of public authorities and the trust and involvement of the population was carried out by conducting factor analysis and constructing a regression model. Due to this, the study proved that the level of trust is more influenced by user engagement, which allows us to show the importance of a qualitative representation of the activities of authorities in social networks to increase the level of trust.

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Bradley, Patrick J. "QUASI-NEWTON MODEL-TRUST REGION APPROACH TO SURROGATE-BASED OPTIMISATION OF PLANAR METAMATERIAL STRUCTURES." Progress In Electromagnetics Research B 47 (2013): 1–17. http://dx.doi.org/10.2528/pierb12100507.

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Wang, Zhaohong, Yaolin Jiang, and Zhen Li. "A trust-region method for optimal H2 model reduction of discrete-time dynamical systems." Journal of Difference Equations and Applications 24, no. 10 (October 3, 2018): 1604–20. http://dx.doi.org/10.1080/10236198.2018.1512980.

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Sato, Kazuhiro, and Hiroyuki Sato. "Structure-Preserving $H^2$ Optimal Model Reduction Based on the Riemannian Trust-Region Method." IEEE Transactions on Automatic Control 63, no. 2 (February 2018): 505–12. http://dx.doi.org/10.1109/tac.2017.2723259.

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Nino-Ruiz, Elias D., Carlos J. Ardila, Alfonso Mancilla, and Jesus Estrada. "A Surrogate Model Based On Mixtures Of Taylor Expansions For Trust Region Based Methods." Procedia Computer Science 108 (2017): 1473–82. http://dx.doi.org/10.1016/j.procs.2017.05.200.

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Walmag, Jérôme M. B., and Éric J. M. Delhez. "A trust-region method applied to parameter identification of a simple prey–predator model." Applied Mathematical Modelling 29, no. 3 (March 2005): 289–307. http://dx.doi.org/10.1016/j.apm.2004.09.005.

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Bakir, Pelin Gundes, Edwin Reynders, and Guido De Roeck. "Sensitivity-based finite element model updating using constrained optimization with a trust region algorithm." Journal of Sound and Vibration 305, no. 1-2 (August 2007): 211–25. http://dx.doi.org/10.1016/j.jsv.2007.03.044.

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Sravan Kumar V., Seshadri, and Thukaram Dhadbanjan. "State estimation in power systems using linear model infinity norm-based trust region approach." IET Generation, Transmission & Distribution 7, no. 5 (May 1, 2013): 500–510. http://dx.doi.org/10.1049/iet-gtd.2012.0473.

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