A general framework for the application of the Newton methods in non-linear coupled electromagnetic-thermal problems solved with the FEM on independent subproblem meshes is presented. The explicit derivation of the Jacobian matrix is outlined and discussed. A matrix-free quasi-Newton method, to be ...
An Overview of Stochastic Quasi-Newton Methods for Large-Scale Machine Learning Feb 2023 Abstract Numerous intriguing optimization problems arise as a result of the advancement of machine learning. The stochastic first-order method is the predominant choice for those problems due to its high efficiency...
In quasi-Newton methods, the matrices Bk are intended to be approximations of F′(xk) and be updated by some quasi-Newton formulas. Another well known algorithm is the trust region type algorithm, for example, [3,4,9,18,19,20,21]. Whether Newton method or quasi-Newton, one has to s...
LP is a special example of SOCP and SOCP is a special case of SDP. SOCP can be solved by the corresponding to the algorithm of SDP, and SOCP also has effectual solving method. Nesterov and Todd [1, 2] had an earlier research on primal-dual interior point method. In the rescent, it...
13 Scientific research on structural color began with the pioneering work of Hooke and Newton in the 17th century. For centuries, structural colors in nature have attracted the attention of researchers. However, it was not until the establishment of electromagnetic theory and the direct observation ...
We solve the coupled system of equations (2.1) by a semi-smooth Newton method [13],based on the propertied of the negative-part-function, combined with a multigrid algorithmfor the linear problems arising in each iteration.Throughout the rest of this paper, we assume that for the solution ...
However, some characteristics of the nonlinear behaviour, such as jump-down frequency and large amplitude excitations, cannot be captured in the semi-analytic solutions by using the Harmonic Balance Method. The transitional force response and rotational moment response with respect to the frequencies of...
Burd, V.S.: Method of Averaging for Differential Equations on an Infinite Interval. CRC Press, Boca Raton (2007) Book MATH Google Scholar Carminati, C.: Forced systems with almost periodic and quasiperiodic forcing term. Nonlinear Anal. Theory Methods Appl. 32(6), 727–739 (1998) Article...
The SUE assignment with elastic demand is solved by using the method of successive averages in conjunction with Bell's matrix inversion logit assignment method. Simple and complex example networks are presented to illustrate the model and the algorithm.系统科学与复杂性学报(英文版)HUANG Haijun School...
Discretization in time is carried out by means of one- and two-step linear A -stable schemes. The resulting system of nonlinear equations is solved by Newton's method. A numerical example is given.doi:10.1002/nme.1620190709Frantis?ek MelkesMilos? Zlámal...