Satisfaction of the strict saddle property has become a standard assumption in non-convex optimization, and it ensures that many first-order optimization algorithms will almost always escape points. However, functions exist machine learning do not satisfy this property, such as loss function neural network with at least two hidden layers. First-order methods gradient descent may converge to non...

For thin plate problems, using the Kirchoff hypothesis, the three dimensional elasticity equations are reduced to a fourth order PDE for the vertical displacement. Conventional FEM has difficulties with this because the basis functions are required to have continuous partial derivatives. Meshfree methods have the advantage of constructing smooth approximation functions, but have difficulties in...

in this letter, the numerical scheme of nonlinear volterra-fredholm integro-differential equations is proposed in a reproducing kernel hilbert space (rkhs). the method is constructed based on the reproducing kernel properties in which the initial condition of the problem is satised. the nonlinear terms are replaced by its taylor series. in this technique, the nonlinear volterra-fredholm integr...

in this paper, we represent an inexact inverse subspace iteration method for com- puting a few eigenpairs of the generalized eigenvalue problem ax = bx[q. ye and p. zhang, inexact inverse subspace iteration for generalized eigenvalue problems, linear algebra and its application, 434 (2011) 1697-1715 ]. in particular, the linear convergence property of the inverse subspace iteration is preserved.