Готові списки джерел за темами / Smoothing Newton method

Добірка наукової літератури з теми "Smoothing Newton method"

Автор: Grafiati

Опубліковано: 18 січня 2023

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Статті в журналах з теми "Smoothing Newton method":

Zhu, Jianguang, and Binbin Hao. "A new smoothing method for solving nonlinear complementarity problems." Open Mathematics 17, no. 1 (March 10, 2019): 104–19. http://dx.doi.org/10.1515/math-2019-0011.

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Abstract In this paper, a new improved smoothing Newton algorithm for the nonlinear complementarity problem was proposed. This method has two-fold advantages. First, compared with the classical smoothing Newton method, our proposed method needn’t nonsingular of the smoothing approximation function; second, the method also inherits the advantage of the classical smoothing Newton method, it only needs to solve one linear system of equations at each iteration. Without the need of strict complementarity conditions and the assumption of P0 property, we get the global and local quadratic convergence properties of the proposed method. Numerical experiments show that the efficiency of the proposed method.

WU, CAIYING, and GUOQING CHEN. "PREDICTOR–CORRECTOR SMOOTHING NEWTON METHOD FOR SOLVING SEMIDEFINITE PROGRAMMING." Bulletin of the Australian Mathematical Society 79, no. 3 (April 17, 2009): 367–76. http://dx.doi.org/10.1017/s0004972708001214.

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AbstractThere has been much interest recently in smoothing methods for solving semidefinite programming (SDP). In this paper, based on the equivalent transformation for the optimality conditions of SDP, we present a predictor–corrector smoothing Newton algorithm for SDP. Issues such as the existence of Newton directions, boundedness of iterates, global convergence, and local superlinear convergence of our algorithm are studied under suitable assumptions.

Feng, Ning, Zhi Yuan Tian, and Xin Lei Qu. "A Smoothing Newton Method for Nonlinear Complementarity Problems." Applied Mechanics and Materials 475-476 (December 2013): 1090–93. http://dx.doi.org/10.4028/www.scientific.net/amm.475-476.1090.

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A new FB-function based on the P0 function is given in this paper. The nonlinear complementarity problem is reformulated to solve equivalent equations based on the FB-function. A modified smooth Newton method is proposed for nonlinear complementarity problem. Under mild conditions, the global convergence of the algorithm is proved. The numerical experiment shows that the algorithm is potentially efficient.

Yong, Longquan. "A Smoothing Newton Method for Absolute Value Equation." International Journal of Control and Automation 9, no. 2 (February 28, 2016): 119–32. http://dx.doi.org/10.14257/ijca.2016.9.2.12.

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Li, Dong-Hui, Liqun Qi, Judy Tam, and Soon-Yi Wu. "A Smoothing Newton Method for Semi-Infinite Programming." Journal of Global Optimization 30, no. 2-3 (November 2004): 169–94. http://dx.doi.org/10.1007/s10898-004-8266-z.

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Tang, Jingyong, Li Dong, Jinchuan Zhou, and Liang Fang. "A smoothing Newton method for nonlinear complementarity problems." Computational and Applied Mathematics 32, no. 1 (March 26, 2013): 107–18. http://dx.doi.org/10.1007/s40314-013-0015-9.

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Li, Meixia, and Haitao Che. "A Smoothing Inexact Newton Method for Generalized Nonlinear Complementarity Problem." Mathematical Problems in Engineering 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/401835.

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Based on the smoothing function of penalized Fischer-Burmeister NCP-function, we propose a new smoothing inexact Newton algorithm with non-monotone line search for solving the generalized nonlinear complementarity problem. We view the smoothing parameter as an independent variable. Under suitable conditions, we show that any accumulation point of the generated sequence is a solution of the generalized nonlinear complementarity problem. We also establish the local superlinear (quadratic) convergence of the proposed algorithm under the BD-regular assumption. Preliminary numerical experiments indicate the feasibility and efficiency of the proposed algorithm.

Qi, L., and D. Sun. "Smoothing Functions and Smoothing Newton Method for Complementarity and Variational Inequality Problems." Journal of Optimization Theory and Applications 113, no. 1 (April 2002): 121–47. http://dx.doi.org/10.1023/a:1014861331301.

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Yin, Hongxia. "An Adaptive Smoothing Method for Continuous Minimax Problems." Asia-Pacific Journal of Operational Research 32, no. 01 (February 2015): 1540001. http://dx.doi.org/10.1142/s0217595915400011.

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A simple and implementable two-loop smoothing method for semi-infinite minimax problem is given with the discretization parameter and the smoothing parameter being updated adaptively. We prove the global convergence of the algorithm when the steepest descent method or a BFGS type quasi-Newton method is applied to the smooth subproblems. The strategy for updating the smoothing parameter can not only guarantee the convergence of the algorithm but also considerably reduce the ill-conditioning caused by increasing the value of the smoothing parameter. Numerical tests show that the algorithm is robust and effective.

Meng, Wei, Zhi Yuan Tian, and Xin Lei Qu. "A Smoothing Method for Solving the NCP Based on a New Smoothing Approximate Function." Applied Mechanics and Materials 462-463 (November 2013): 294–97. http://dx.doi.org/10.4028/www.scientific.net/amm.462-463.294.

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A new smoothing approximate function of the FischerBurmeister function is given. A modified smoothing Newton method based on the function is proposed for solving a kind of nonlinear complementarity problems. Under suitable conditions, the global convergence of the method is proved. Numerical results show the effectiveness of the method.

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Дисертації з теми "Smoothing Newton method":

Ferzly, Joëlle. "Adaptive inexact smoothing Newton method for nonlinear systems with complementarity constraints. Application to a compositional multiphase flow in porous media." Thesis, Sorbonne université, 2022. http://www.theses.fr/2022SORUS376.

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Nous considérons des inégalités variationnelles écrites sous forme d'équations aux dérivées partielles avec contraintes de complémentarité non linéaires. La discrétisation de tels problèmes conduit à des systèmes discrets non linéaires et non différentiables qui peuvent être résolus en employant une méthode de linéarisation itérative de type semi-lisse. Notre objectif est de concevoir une approche de régularisation qui approxime le problème par un système d'équations non linéaires différentiables. Une application directe des méthodes classiques de type Newton est ainsi possible. Nous construisons des estimations d'erreur a posteriori qui sont à la base d'un algorithme de Newton régularisé, inexact et adaptatif, pour une solution des problèmes considérés. Dans le chapitre 1, dans un cadre discret, nous nous intéressons aux systèmes algébriques non linéaires avec des contraintes de complémentarité provenant de discrétisations numériques d'EDP avec problèmes de complémentarité. Nous produisons une approximation différentiable d'une fonction non différentiable, en reformulant les conditions de complémentarité. Le système non linéaire qui en résulte est résolu par la méthode de Newton, ainsi qu'un solveur algébrique linéaire itératif. Nous établissons une borne supérieure sur le résidu du système considéré et concevons des estimateurs d'erreur a posteriori identifiant les composantes d'erreur de régularisation, de linéarisation et algébrique. Ces ingrédients sont utilisés pour formuler des critères d'arrêt efficaces pour les solveurs non linéaires et algébriques. Avec la même méthodologie, une méthode adaptative de points intérieurs est proposée. Nous appliquons notre algorithme au système algébrique d'inégalités variationnelles décrivant le contact entre deux membranes et à un problème d'écoulement diphasique. Nous fournissons une comparaison numérique de notre approche avec une méthode de Newton semi-lisse, éventuellement combinée avec une stratégie de path-following, et une méthode non-paramétrique de points intérieurs. Dans le chapitre 2, en dimension infinie, nous considérons le problème de contact entre deux membranes. Nous utilisons une discrétisation par la méthode des volumes finis et appliquons l'approche de régularisation proposée dans le chapitre 1 pour lisser la non-différentiabilité dans les contraintes de complémentarité. La résolution du système régularisé non linéaire qui en résulte est réalisée grâce à la méthode de Newton, en combinaison avec un solveur algébrique itératif. Nous concevons des reconstructions de potentiel H1-conformes et des reconstructions de flux équilibrés discrets H(div)-conformes. Nous prouvons une borne supérieure pour l'erreur totale par la norme d'énergie et concevons des estimateurs reflétant les erreurs provenant de la discrétisation en volumes finis, du lissage de la non-différentiabilité, de la linéarisation par la méthode de Newton et du solveur algébrique, respectivement. Cela nous permet d'établir des critères d'arrêt adaptatifs pour arrêter les différents solveurs dans l'algorithme proposé et de concevoir un algorithme adaptatif pilotant ces quatre composantes. Dans le chapitre 3, nous introduisons une application à un modèle industriel d’écoulement multiphasique compositionnel avec transitions de phase en milieu poreux. Une discrétisation par la méthode des volumes finis produit un système algébrique non linéaire et non différentiable que nous résolvons en utilisant notre technique de Newton régularisé et inexacte. En suivant le processus du chapitre 1, nous construisons des estimateurs a posteriori en majorant la norme du résidu du système discret, ce qui résulte des critères adaptatifs que nous incorporons dans l'algorithme employé. Des expériences numériques confirment l'efficacité de nos estimations. En particulier, nous montrons que les algorithmes adaptatifs développés réduisent significativement le nombre global d'itérations par rapport aux méthodes existantes
We consider variational inequalities written in the form of partial differential equations with nonlinear complementarity constraints. The discretization of such problems leads to nonlinear non-differentiable discrete systems that can be solved employing an iterative linearization method of semismooth type like, e.g., the Newton-min algorithm. Our goal in this thesis is to conceive a simple smoothing approach that involves approximating the problem as a system of nonlinear smooth (differentiable) equations. In this setting, a direct application of classical Newton-type methods is possible. We construct a posteriori error estimates that lie at the foundation of an adaptive inexact smoothing Newton algorithm for a solution of the considered problems. We first present the strategy in a discrete framework. Then, we develop the method for the model problem of contact between two membranes. Last, an application to a compositional multiphase flow industrial model is introduced. In Chapter 1, we are concerned about nonlinear algebraic systems with complementarity constraints arising from numerical discretizations of PDEs with nonlinear complementarity problems. We produce a smooth approximation of a nonsmooth function, reformulating the complementarity conditions. The ensuing nonlinear system is solved employing the Newton method, together with an iterative linear algebraic solver to approximately solve the linear system. We establish an upper bound on the considered system’s residual and design a posteriori error estimators identifying the smoothing, linearization, and algebraic error components. These ingredients are used to formulate efficient stopping criteria for the nonlinear and algebraic solvers. With the same methodology, an adaptive interior-point method is proposed. We apply our algorithm to the algebraic system of variational inequalities describing the contact between two membranes and a two-phase flow problem. We provide numerical comparison of our approach with a semismooth Newton method, possibly combined with a path-following strategy, and a nonparametric interior-point method. In Chapter 2, in an infinite-dimensional framework, we consider as a model problem the contact problem between two membranes. We employ a finite volume discretization and apply the smoothing approach proposed in Chapter 1 to smooth the non-differentiability in the complementarity constraints. The resolution of the arising nonlinear smooth system is again realized thanks to the Newton method, in combination with an iterative algebraic solver for the solution of the resulting linear system. We design H1-conforming potential reconstructions as well as H(div)-conforming discrete equilibrated flux reconstructions. We prove an upper bound for the total error in the energy norm and conceive discretization, smoothing, linearization, and algebraic estimators reflecting the errors stemming from the finite volume discretization, the smoothing of the non-differentiability, the linearization by the Newton method, and the algebraic solver, respectively. This enables us to establish adaptive stopping criteria to stop the different solvers in the proposed algorithm and design adaptive algorithm steering all these four components. In Chapter 3, we consider a compositional multiphase flow (oil, gas, and water) with phase transitions in a porous media. A finite volume discretization yields a nonlinear non-differentiable algebraic system which we solve employing our inexact smoothing Newton technique. Following the process of Chapter 1, we build a posteriori estimators by bounding the norm of the discrete system’s residual, resulting in adaptive criteria that we incorporate in the employed algorithm. Throughout this thesis, numerical experiments confirm the efficiency of our estimates. In particular, we show that the developed adaptive algorithms considerably reduce the overall number of iterations in comparison with the existing methods

Lin, Tzu-Ching, and 林子靖. "A smoothing Newton method based on the generalized Fischer-Burmeister function for MCPs." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/hg76p7.

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碩士
國立臺灣師範大學
數學系
97
We present a smooth approximation for the generalized Fischer-Burmeister function where the 2-norm in the FB function is relaxed to a general p-norm (p > 1), and establish some favorable properties for it, for example, the Jacobian consistency. With the smoothing function, we transform the mixed complementarity problem (MCP) into solving a sequence of smooth system of equations.

Книги з теми "Smoothing Newton method":

Ulbrich, Michael, Liqun Qi, and Defeng Sun. Semismooth and Smoothing Newton Methods. Springer, 2021.

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Частини книг з теми "Smoothing Newton method":

Zhang, Jie, and Shao-Ping Rui. "Globally Convergent Inexact Smoothing Newton Method for SOCCP." In Advances in Intelligent and Soft Computing, 427–34. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22833-9_52.

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Solodov, Michael V., and Benav F. Svaiter. "A Globally Convergent Inexact Newton Method for Systems of Monotone Equations." In Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, 355–69. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4757-6388-1_18.

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Liu, Lixia, and Sanyang Liu. "A New Smoothing Newton Method for Symmetric Cone Complementarity Problems." In Algorithmic Aspects in Information and Management, 199–208. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14355-7_21.

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Chen, Weibing, Hongxia Yin, and Yingjie Tian. "Smoothing Newton Method for L 1 Soft Margin Data Classification Problem." In Lecture Notes in Computer Science, 543–51. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-01973-9_61.

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Qi, L., and G. Zhou. "A Smoothing Newton Method for Ball Constrained Variational Inequalities with Applications." In Topics in Numerical Analysis, 211–25. Vienna: Springer Vienna, 2001. http://dx.doi.org/10.1007/978-3-7091-6217-0_16.

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Fang, Liang, Xianming Kong, Xiaoyan Ma, Han Li, and Wei Zhang. "A One-Step Smoothing Newton Method Based on a New Class of One-Parametric Nonlinear Complementarity Functions for P 0-NCP." In Advances in Neural Networks - ISNN 2010, 110–17. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-13278-0_15.

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Chen, Xiaojun, Nami Matsunaga, and Tetsuro Yamamoto. "Smoothing Newton Methods for Nonsmooth Dirichlet Problems." In Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, 65–79. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4757-6388-1_4.

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Christensen, Peter W., and Jong-Shi Pang. "Frictional Contact Algorithms Based on Semismooth Newton Methods." In Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, 81–116. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4757-6388-1_5.

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Li, Wu, and John Swetits. "Regularized Newton Methods for Minimization of Convex Quadratic Splines with Singular Hessians." In Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, 235–57. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4757-6388-1_12.

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Qi, L., and D. Sun. "A Survey of Some Nonsmooth Equations and Smoothing Newton Methods." In Applied Optimization, 121–46. Boston, MA: Springer US, 1999. http://dx.doi.org/10.1007/978-1-4613-3285-5_7.

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Тези доповідей конференцій з теми "Smoothing Newton method":

Yu, Haodong. "A Smoothing Active-Set Newton Method for Constrained Optimization." In 2012 Fifth International Joint Conference on Computational Sciences and Optimization (CSO). IEEE, 2012. http://dx.doi.org/10.1109/cso.2012.95.

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Jiang, Xiaoqin. "A Smoothing Newton Method for Solving Absolute Value Equations." In 2nd International Conference On Systems Engineering and Modeling. Paris, France: Atlantis Press, 2013. http://dx.doi.org/10.2991/icsem.2013.94.

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Chi, Xiaoni, and Xiaoyong Liao. "A Squared Smoothing Newton Method for Second-Order Cone Programming." In 2010 Third International Conference on Information and Computing Science (ICIC). IEEE, 2010. http://dx.doi.org/10.1109/icic.2010.185.

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Su, Ke, and Xiaoli Lu. "A New Smoothing Inexact Newton Method for Generalized Nonlinear Complementarity Problem." In 2013 Sixth International Conference on Business Intelligence and Financial Engineering (BIFE). IEEE, 2013. http://dx.doi.org/10.1109/bife.2013.130.

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Yousefian, Farzad, Angelia Nedic, and Uday V. Shanbhag. "A smoothing stochastic quasi-newton method for non-lipschitzian stochastic optimization problems." In 2017 Winter Simulation Conference (WSC). IEEE, 2017. http://dx.doi.org/10.1109/wsc.2017.8247960.

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Zhao, Huali, and Hongwei Liu. "Predictor-Corrector Smoothing Newton Method for Solving the Second-Order Cone Complementarity." In 2010 International Conference on Intelligent Computation Technology and Automation (ICICTA). IEEE, 2010. http://dx.doi.org/10.1109/icicta.2010.590.

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He, Yanling, and Chunyan Liu. "Sub-quadratic convergence of a smoothing Newton method for symmetric cone complementarity problems." In 2015 27th Chinese Control and Decision Conference (CCDC). IEEE, 2015. http://dx.doi.org/10.1109/ccdc.2015.7162450.

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Zhao, Hua-Li, and Hong-Wei Liu. "A Predictor-corrector Smoothing Newton Method for Solving the Second-order Cone Complementarity." In 2010 International Conference on Computational Aspects of Social Networks (CASoN 2010). IEEE, 2010. http://dx.doi.org/10.1109/cason.2010.66.

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Hao, Muting, Feng Wang, Joshua Hope-Collins, Max E. Rife, and Luca di Mare. "Template-Based Hexahedral Mesh Generation for Turbine Cooling Geometries." In ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/gt2020-14660.

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Abstract This paper describes a multiblock grid generation method for turbine cooling geometries. The method is based on the observation that cooling films are essentially branches inserted on a large trunk, represented by the passage or by the cooling duct. The small size of the films compared to the overall size of turbine blades allows simplifications to be introduced with respect to general-purpose trunk and branch algorithms. The grid generation starts from an existing layout for the passage or cooling duct grid and operates on a Cartesian patch of the trunk surface. The patch is hollowed and a templated branch layout is inserted. Padding blocks are created to connect the two layouts into a single, boundary conforming layout. The resulting multiblock grid is then smoothed using a modification of Thompson’s Poisson system. The boundary mesh distribution is not prescribed. Instead, boundary orthogonality is enforced and elliptic smoothing is performed on the boundaries as well as inside the volume. The grid size control relies on a novel Newton-like update for the control functions of the Poisson system. The smoothing step is essential in achieving good grid quality throughout and determines, in part, the template for a given configuration. The algorithm is particularly suitable for large arrays of films or other cooling decoration and results show that the proposed method can produce grids of better quality than existing methods.

Kumar, Prabhat, Roger A. Sauer, and Anupam Saxena. "On Synthesis of Contact Aided Compliant Mechanisms Using the Material Mask Overlay Method." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-47064.

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Contact Aided Compliant Mechanisms (CCMs) are synthesized via the Material Mask Overlay Strategy (MMOS) to trace a desired non-smooth path. MMOS employs hexagonal cells to discretize the design region and engages negative circular masks to designate material states. To synthesize CCMs, the modified MMOS presented herein involves systematic mutation of five mask parameters through a hill climber search to evolve not only the continuum topology (slave surfaces), but also, to introduce the desired rigid, interacting surfaces within some masks. Various geometric singularities are subdued via hexagonal cells though numerous V-notches get retained at the continuum boundaries. To facilitate contact analysis, boundary smoothing is performed by shifting boundary nodes of the evolving continuum systematically. Numerous hexagonal cells get morphed into concave sub-regions as a consequence. Large deformation finite element formulation with Mean Value Coordinates (MVC) based shape functions is used to cater to the generic hexagonal shapes. Contact analysis is accomplished via the Newton-Raphson iterations with load increment in conjunction with the penalty method and active set constraints. An objective function based on Fourier Shape Descriptors is minimized subject to suitable design constraints. An example of a path generating CCM is included to establish the efficacy of the proposed synthesis method.