A new method is presented for numerically capturing a moving interface of arbitrary dimension and codimension. The method is named the ‘local level set method’, since it localizes the level set method near the interface to significantly reduce the computational expense of the level set method. Following the framework of the level set method, an interface is implicitly represented as the zero le...

Let H : <m×<n → <n be a locally Lipschitz function in a neighborhood of (ȳ, x̄) and H(ȳ, x̄) = 0 for ȳ ∈ <m and x̄ ∈ <n. The implicit function theorem in the sense of Clarke [1, 2] says that if πx∂H(ȳ, x̄) is of maximal rank, then there exist a neighborhood Y of ȳ and a Lipschitz function G(·) : Y → <n such that G(ȳ) = x̄ and for every y in Y , H(y,G(y)) = 0. In this paper, we shall further show tha...

In this paper we present stability and sensitivity analysis of a stochastic optimization problem with stochastic second order dominance constraints. We consider perturbation of the underlying probability measure in the space of regular measures equipped with pseudometric discrepancy distance ( [30]). By exploiting a result on error bound in semi-infinite programming due to Gugat [13], we show u...

This paper considers the distributed optimization of a sum of locally observable, nonconvex functions. The optimization is performed over a multi-agent networked system, and each local function depends only on a subset of the variables. An asynchronous and distributed alternating directions method of multipliers (ADMM) method that allows the nodes to defer or skip the computation and transmissi...

Output global finite-time stability of locally Lipschitz continuous autonomous systems is characterized by means smooth Lyapunov functions. The so-called output-Lagrange stable are studied with details. Influence a kind continuity the settling-time function considered. Necessary and sufficient conditions output presented. theoretical results supported academic examples numerical simulations.

We propose a generalized Newton method for solving the system of nonlinear equations with linear complementarity constraints in the implicit or semi-implicit time-stepping scheme for differential linear complementarity systems (DLCS). We choose a specific solution from the solution set of the linear complementarity constraints to define a locally Lipschitz continuous right-hand-side function in...

We extend the taming techniques for explicit Euler approximations of stochastic differential equations (SDEs) driven by Lévy noise with super-linearly growing drift coefficients. Strong convergence results are presented for the case of locally Lipschitz coefficients. Moreover, rate of convergence results are obtained in agreement with classical literature when the local Lipschitz continuity ass...

We propose a class of locally Lipschitz functions with piecewise structure for use as Lyapunov hybrid dynamical systems. Subject to some regularity the dynamics, we show that inequalities can be checked only on dense set and thus avoid checking them at points nondifferentiability function. Connections other classes or regular are also discussed, applications systems included.

We prove that any 2-dimensional solution ψ ∈ W 1+ 1 3,3 loc of the eikonal equation has locally Lipschitz gradient ∇ψ except at a locally finite number of vortex-points. A related regularizing effect is also obtained for general solutions of the Burgers’ equation. DOI: https://doi.org/10.1080/03605302.2014.999939 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: h...