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 ...
We propose a semismooth Newton-type method for nonsmooth optimal control problems. Its particular feature is the combination of a quasi-Newton method with
Equation (8) is the basis of the analysis developed in this work. It states that we can study quasi-Newton steps using the Jacobian of the Newton step. The only difference is the right-hand side. Using this property of the Broyden “bad” update we are able to extend the well known c...
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...
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...
(33)). On the other hand, it is addressed to avoid the computation of the consistent tangent stiffness matrix necessary for the application of the Newton Raphson method. In fact, in the case of the constitutive d+/d− damage model here presented, this matrix is non-symmetric and requires...
In this section, the “multiple shooting method + SQP method” is used to solve the shapes and internal force of the bubble and the “membrane bundle system”. Firstly, the main zero-pressure balloon and ground launching parameters involved in the calculation example are introduced in Table 1....
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...
For example, pure Weyl-squared gravity allows for four dimensional solutions with N = 1 [34, 37–39]. 3. Further, the theory must admit an Einstein-Gravity limit, i.e. reduce to the Einstein- Hilbert action upon setting some of the parameters in the action to zero. This excludes ...
For example, it has recently been shown that the most general cubic theory of gravity which propagates the same degrees of freedom as Ein- stein gravity and has the same form in all dimensions includes, in addition to cubic Lovelock gravity, an additional cubic term which has been dubbed ...