We study the equation ut + uux + u − K * u = 0 in the case of an arbitrary K ≥ 0, which is a generalization of a model for radiating gas, in which K(y) = 1 2 e −|y|. Using a monotone iteration scheme argument we establish the existence of traveling waves, which gives a solution to an open question raised by Denis Serre [1].

We derive fast solvers for discrete elliptic variational inequalities of the rst kind (obstacle problems) as resulting from the approximation of related continuous problems by piecewise linear nite elements. Using basic ideas of successive subspace correction, we modify well-known relaxation methods by extending the set of search directions. Extended underrelaxations are called monotone multigr...

zero point problems of the sum of two monotone mappings and fixed point problems of a strictly pseudocontractive mapping are investigated‎. ‎a strong convergence theorem for the common solutions of the problems is established in the framework of hilbert spaces‎.

‎In this paper‎, ‎some properties of pre-monotone operators are proved‎. ‎It is shown that in a reflexive Banach space‎, ‎a full domain multivalued $sigma$-monotone operator with sequentially norm$times$weak$^*$ closed graph is norm$times$weak$^*$ upper semicontinuous‎. ‎The notion of $sigma$-convexity is introduced and the‎ ‎relations between the $sigma$-monotonicity and $sigma$-convexity is i...

This paper describes an accelerated HPE-type method based on general Bregman distances for solving monotone saddle-point (SP) problems. The algorithm is a special instance of a non-Euclidean hybrid proximal extragradient framework introduced by Svaiter and Solodov [28] where the prox sub-inclusions are solved using an accelerated gradient method. It generalizes the accelerated HPE algorithm pre...

We consider a generalized proximal point method (GPPA) for solving the nonlinear complementarity problem with monotone operators in R ' \ lt differs from the classical proximal point method discussed by Rockafellar for the problem offinding zeroes of monotone operators in the use of generalized distances, called (p-divergences, instead of the Euclidean one. These distances play not only a regul...

The existence of polynomial-size (monotone) formulae is known to be equivalent to the existence of logarithmic-depth (monotone) circuits of bounded fan-in. Anyhow, we shall prove the existence of logarithmic-depth monotone formulae (of bounded fan-in) for majority. Actually, two radically different proofs are known: The first proof uses a rather complicated construction of sorting networks of l...

In this note we show that the splitting scheme of Passty [7] as well as the barycentric-proximal method of Lehdili & Lemaire [4] can be used to approximate a zero of the extended sum of maximal monotone operators. When the extended sum is maximal monotone, we extend the convergence result obtained by Lehdili & Lemaire for convex functions to the case of maximal monotone operators. Moreover, we ...

The monotone secant conjecture posits a rich class of polynomial systems, all of whose solutions are real. These systems come from the Schubert calculus on flag manifolds, and the monotone secant conjecture is a compelling generalization of the Shapiro conjecture for Grassmannians (Theorem of Mukhin, Tarasov, and Varchenko). We present some theoretical evidence for this conjecture, as well as c...

in this paper we propose a descent method for solving variational inequality problems where the underlying operator is nonsmooth, locally Lipschitz, and monotone over a closed, convex feasible set. The idea is to combine a descent method for variational inequality problems whose operators are nonsmooth, locally Lipschitz, and strongly monotone, with the Tikonov-Browder regularization technique....