Second-order L∞ variational problems and the ∞-polylaplacian

Modified Variational Iteration Method for Second Order Initial Value Problems

In this paper, we introduce a modified variational iteration method for second order initial value problems by transforming the integral of iteration process. The main advantages of this modification are that it can overcome the restriction of the form of nonlinearity term in differential equations and improve the iterative speed of conventional variational iteration method. The method is appli...

Higher Order Variational Problems

Higher order variational problems appear often in the engineering literature and in connection with the so-called gradient theories of phase transitions within elasto-plastic regimes. The study of equilibria of micromagnetic materials asks for mastery of second order energies (see [51], [91]; see also [31], [38], [44], [45], [61], [77], [78], [79], [108]), and the Blake-Zisserman model for imag...

Second-order stochastic variational inference

Stochastic gradient descent (SGD), the workhorse of stochastic optimization, is slow in theory (sub-linear convergence) and in practice (thousands of iterations), intuitively for two reasons: 1) Its learning rate schedule is fixed a priori and decays rapidly enough to 0 that is square-summable. This learning rate schedule limits the step size and hence the rate of convergence for a Lipschitz ob...

L ∞ - convergence of saddle - point approximations for second order problems

Initial value problems for second order hybrid fuzzy differential equations

Usage of fuzzy differential equations (FDEs) is a natural way to model dynamical systems under possibilistic uncertainty. We consider second order hybrid fuzzy differentia