We consider nonlinear nonconvex evolution inclusions driven by time-varying subdifferentials 0(t,x) without assuming that (t,.) is of compact type. We show the existence of extremal solutions and then we prove a strong relaxation theorem. Moreover,r we show that under a Lipschitz condition on the orientor field, the solution set of the nonconvex problem is path-connected in C(T,H). These result...

In this study, we introduce a new generalization of Bernstein-type rational function possessing better estimates than the classical function. We investigate its error approximation globally and locally in terms first second modulus continuity class Lipschitz-type functions. present graphical comparisons with illustrative examples.

This paper addresses rate control for transmission of scalable video streams via Network Utility Maximization (NUM) formulation. Due to stringent QoS requirements of video streams and specific characterization of utility experienced by end-users, one has to solve nonconvex and even nonsmooth NUM formulation for such streams, where dual methods often prove incompetent. Convexification plays an i...

We prove the existence of solutions for the differential inclusion ẋ(t) ∈ F (t, x(t)) + f(t, x(t)) for a multifunction F upper semicontinuous with compact values contained in the generalized Clarke gradient of a regular locally Lipschitz function and f a Carathéodory function.

We adapt the Douglas-Rachford (DR) splitting method to solve nonconvex feasibility problems by studying this method for a class of nonconvex optimization problem. While the convergence properties of the method for convex problems have been well studied, far less is known in the nonconvex setting. In this paper, for the direct adaptation of the method to minimize the sum of a proper closed funct...

The paper summarizes the main core of last results that we obtained in [8, 4, 17] on regularity value function for a Bolza problem one-dimensional, vectorial calculus variations. We are concerned with nonautonomous Lagrangian is possibly highly discontinuous state and velocity variables, nonconvex variable non coercive. achieved under assumption convex one-dimensional lines satisfies local Lips...

A class of nonlinear Neumann problems driven by p(x)-Laplacian with a nonsmooth locally Lipschitz potential (hemivariational inequality) was considered. The approach used in this paper is the variational method for locally Lipschitz functions. More precisely, Weierstrass theorem and Mountain Pass theorem are used to prove the existence of at least two nontrivial solutions.

This paper proposes the Proximal Iteratively REweighted (PIRE) algorithm for solving a general problem, which involves a large body of nonconvex sparse and structured sparse related problems. Comparing with previous iterative solvers for nonconvex sparse problem, PIRE is much more general and efficient. The computational cost of PIRE in each iteration is usually as low as the state-of-the-art c...

A global regularity theorem for stress fields which correspond to minimisers of convex and some special nonconvex variational problems is derived for Lipschitz-domains. In the first part it is assumed that the energy densities defining the variational problem are convex but not necessarily strictly convex and satisfy a convexity inequality. The regularity result for this case is derived with a ...

Under usual assumptions on the Hamiltonian, we prove that any viscosity solution of the corresponding Hamilton-Jacobi equation on the manifold M is locally semiconcave and C loc outside the closure of its singular set (which is nowhere dense in M). Moreover, we prove that, under additional assumptions and in low dimension, any viscosity solution of that Hamilton-Jacobi equation satisfies a gene...