Showing papers on "Strongly monotone published in 1989"
TL;DR: In this article, the authors consider des equations paraboliques semi-lineaires: dy/dt+Ay=f(y), ou A est un operateur sectoriel sur un Banach X ayant une resolvante compacte and f est une C 2 -application de l'espace des puissances fractionnaires Xα, 0≤α<1, dans X. Alors il existe an voisinage U de y 0 =y(0) avec la propriete suivante: si z∈U\
89 citations
TL;DR: In this article, the basic Newton method is modified to yield an algorithm whose global convergence can be guaranteed by monitoring the monotone decrease of the "gap function" associated with the variational inequality.
Abstract: Applied to strongly monotone variational inequalities, Newton’s algorithm achieves local quadratic convergence. In this paper it is shown how the basic Newton method can be modified to yield an algorithm whose global convergence can be guaranteed by monitoring the monotone decrease of the “gap function” associated with the variational inequality. Each iteration consists in the solution of a linear program in the space of primal-dual variables and of a linesearch. Convergence does not depend on strong monotonicity. However, under strong monotonicity and geometric stability assumptions, the set of active constraints at the solution is implicitly identified, and quadratic convergence is achieved.
44 citations
01 Jan 1989
TL;DR: In this paper, the correspondence between operator monotone functions and Stieltjes functions was investigated and it was shown that the class of nonnegative nonnegative operator monotonone functions is closed under certain operations, and applying those they decide the case when some binary operations become operator means.
Abstract: We investigate the correspondence between operator monotone functions and Stieltjes functions. Then we shall prove that the class of nonnegative operator monotone functions is closed under certain operations, and applying those we decide the case when some binary operations become operator means.
35 citations
TL;DR: In this article, l'action α du groupe G est monotone, alors la symetrie est incluse dans le comportement non chaotique.
Abstract: Si l'action α du groupe G est monotone, alors la symetrie est incluse dans le comportement non chaotique
10 citations
TL;DR: In this paper, the convergence of variational inequalities for monotone operators is studied when both the operator and the obstacle are perturbed, and some new results on the convergence are proved.
Abstract: We prove some new results on the convergence of variational inequalities for monotone operators, when both the operator and the obstacle are perturbed
10 citations
01 Apr 1989
TL;DR: In this article, it was shown that each precompact orbit of strongly monotone dynamical systems on a Banach lattice X is convergent if there is a continuous map e: X -+ E, the set of equilibria, such that e(x) is the maximal element in X with e(n) 0, f: R -+ R is continuous and increasing; or the following partial differential equation au = Au + g(x, u, Vu), t>O, xEQ (2) u(x 0, 0
Abstract: We show that each precompact orbit of strongly monotone dynamical systems on a Banach lattice X is convergent if there is a continuous map e: X -+ E, the set of equilibria, such that e(x) is the maximal element in E with e(x) 0, f: R -+ R is continuous and increasing; or the following partial differential equation au = Au + g(x, u, Vu), t>O, xEQ (2) u(x, 0) = v(x), x E Q, u(x, t) = 0 xEaQ, t>O an where Q is a bounded smooth domain in Rn, A is a second-order uniformly elliptic differential operator and g: Q x R x Rn + R is locally Lipschitz and satisfies g(x,c,O) = 0 for any x E Q and c E R, au/an is the derivative of u in the direction of the outward normal to Q For these equations, each Received by the editors October 3, 1988 and, in revised form December 2, 1988 1980 Mathematics Subject Classification (1985 Revision) Primary 06F05, 34K20, 34K25, 34C35, 35K10, 58F10, 92A15 (?) 1989 American Mathematical Society 0002-9939/89 $100 + S25 per page
9 citations
TL;DR: In this paper, a completely discretized variational problem corresponding to a nonlinear second order parabolic-elliptic initial-boundary value problem with an initial value only inL 2 is presented.
Abstract: The study of a completely discretized variational problem corresponding to a nonlinear second order parabolic-elliptic initial-boundary value problem with an initial value only inL 2 is presented. The discretization in time is done by the Euler backward method, the discretization in space by the finite element method with linear functions on triangular elements. The changes in domain are taken into account. The convergence and the unconditional stability of the method is proved under the assumption that the boundary ?Ω is piecewise of classC 3 and the forma(v, w) has a potential and is strongly monotone and Lipschitz continuous. As a by-product the existence and uniqueness theorem is obtained.
8 citations
TL;DR: A broad class of monotone Boolean functions is examined, proving that for almost all of the functions in the class, no such simulation exists, and that in a very weak sense negation is exponentially powerful.
6 citations
TL;DR: The Cauchy problem has analytic solutions whenA has first and second Gateaux derivatives along the solution curve in a certain weak sense as mentioned in this paper, where A is a maximal monotone operator in a complex Hilbert space.
Abstract: The Cauchy problemdu/dt =Au(t),u(0) =u
0∈D(A) has analytic solutions whenA has first and second Gateaux derivatives along the solution curve in a certain weak sense. HereA is a maximal monotone operator in a complex Hilbert space.
5 citations
TL;DR: In this article, the authors used the shooting method to prove existence and uniqueness of the solution for a semilinear Sturm-Liouville boundary value problem (N).
Abstract: The shooting method is used to prove existence and uniqueness of the solution for a semilinear Sturm-Liouville boundary value problem (N).\(\frac{\partial }{{\partial u}}f(x,u)\) “lies between two consecutive eigenvalues” of the related linear problem, the shooting function turns out to be strongly monotone.
4 citations
TL;DR: In this paper, the existence of slow and monotone solutions with respect to a continuous pre-order is proved for differential inclusions defined on a closed convex subset of R4.
Abstract: The existence of slow and monotone solutions with respect to a continuous pre-order is proved for differential inclusions defined on a closed convex subset of R4. First we examine the ‘projected system’, and prove that it is equivalent to a differential variational inequality. We then establish the existence of monotone trajectories. Subsequently, we prove the existence of slow monotone solutions for a class of differential inclusions, satisfying a Nagumo-type condition. Finally we prove a convergence result.
TL;DR: In this article, sufficient conditions involving the Cech cohomology of point-inverses are given to insure that a monotone map between compact metric spaces admits a restriction which remains a monotonous map with the same image as the original map.
TL;DR: In this paper, the best L ∞ -simultaneous approximant of f and g is defined as an element h * ∈ M satisfying for all h ∈ m, where the value of d is defined in terms of f, g and w only.
Abstract: Let X = [ a, b ] be a closed bounded real interval. Let B be the closed linear space of all bounded real valued functions defined on X , and let M ⊆ B be the closed convex cone consisting of all monotone non-decreasing functions on X . For f, g ∈ B and a fixed positive w ∈ B , we define the so-called best L ∞ -simultaneous approximant of f and g to be an element h * ∈ M satisfying for all h ∈ M , where We establish a duality result involving the value of d in terms of f, g and w only. If in addition f , g and w are continuous, then some characterisation results are obtained.
01 Jan 1989
11 Jul 1989
TL;DR: It is shown that the time to compute a monotone boolean function depending upon n variables on a CREW-PRAM satisfies the lower bound T=Θ(logl+(log n)/l), where l is the size of the largest prime implicant.
Abstract: It is shown that the time to compute a monotone boolean function depending upon n variables on a CREW-PRAM satisfies the lower bound T=Θ(logl+(log n)/l), where l is the size of the largest prime implicant. It is also shown that the bound is existentially tight by constructing a family of monotone functions that can be computed in T=O(log l+(log n)/l), even by an EREW-PRAM. The same results hold if l is replaced by L, the size of the largest prime clause.