Showing papers on "Strongly monotone published in 1984"
TL;DR: It is shown that the monotone formula-size complexity of themonotone symmetric functions on n variables can be bounded above by a function of order O ( n 5.3 ).
248 citations
01 Jan 1984
68 citations
01 Dec 1984
TL;DR: An exponential lower bound for the majority function on constant depth monotone circuits is proved, solving an open problem of A. Yao's problem and getting exponential lower bounds for other problems, such as connectivity and cliques.
Abstract: We prove an exponential lower bound for the majority function on constant depth monotone circuits, solving an open problem of A. Yao's.. In particular, we prove that computing majority on depth d monotone circuits requires expΩ(n1/(d-1)) size. Using this result we also get exponential lower bounds for other problems, such as connectivity and cliques.
30 citations
TL;DR: In this paper a special function is presented for which a lower bound of size 4n over the monotone basis can be proved.
20 citations
TL;DR: In this article, it was shown that for strongly monotone operators, the truncation errors are bounded uniformly in time and with error O(Δt)2, ifϑ = 1/2−|O( Δt)|, where Δt is the Lipschitz constant.
Abstract: Classical discretization error estimates for systems of ordinary differential equations contain a factor exp (Lt), whereL is the Lipschitz constant. For strongly monotone operators, however, one may prove that for aϑ-method, 0<ϑ<1/2, the errors are bounded uniformly in time and with errorO(Δt)2, ifϑ=1/2−|O(Δt)|. This was done by this author (1977), for an operator in a reflexive Banach space and includes the case of systems of differential equations as a special case. In the present paper we restate this result as it may have been overlooked and consider also the monotone (inclusive of the conservative) and unbounded cases. We also discuss cases where the truncation errors are bounded by a constant independent of the stiffness of the problem. This extends previous results in [6] and [7]. Finally we discuss a boundary value technique in the context above.
15 citations
TL;DR: In this article, the authors consider the quasiautonomous initial value problem and investigate the injectiveness of the mapping f ~ u r r, where u r is the solution of f ( t ) E u'(t) + Au.
Abstract: Let A be a maximal monotone operator. Let u: be the solution of f ( t ) E u'(t) + Au. We investigate the injectiveness of the mapping f ~ u r. In this note we consider the quasiautonomous initial value problem f ( t )~u ' ( t )+Au( t ) (a _-< t < ~ ) , (1) x = u(a), where A is a maximal monotone operator in a Hilbert space (H, I I). Here x ED(A) , a GR, and f:R---~H is assumed to be locally integrable. For any such A, x, a, jr, it is well known that (1) has a unique solution ut : [a, ~)---~ D(A). The solution depends continuously on the data, in the following sense: (2) lut(t)-ug(t)l~=tut(a)-u,(a)l+ I[(s)-g(s)lds (a_-
2 citations
1 citations
01 Jan 1984
TL;DR: In this article, the generalized monotone linear complementarity problem in reflexive Banach space is studied and the problem is treated as a quadratic program and shown to satisfy appropriate constraint qualifications.
Abstract: We study the (monotone) linear complementarity problem in reflexive Banach space. The problem is treated as a quadratic program and shown to satisfy appropriate constraint qualifications. This leads to a theory of the generalized monotone linear complementarity problem which is independent of Brouwer's fixed-point theorem. Certain related results on linear systems are given. The final section concerns copositive operators.
1 citations