Global optimization of multivariable functions satisfying the Vanderbei condition

On functions with the derivative satisfying a geometric condition

In this paper, we prove some properties of the analytic functions whose derivatives takes values outside of a parabola. Some applications are given. 2008 Elsevier Inc. All rights reserved.

Global optimization of Lipschitz functions

The goal of the paper is to design sequential strategies which lead to efficient optimization of an unknown function under the only assumption that it has a finite Lipschitz constant. We first identify sufficient conditions for the consistency of generic sequential algorithms and formulate the expected minimax rate for their performance. We introduce and analyze a first algorithm called LIPO wh...

On ℤ4 codes satisfying the chain condition

Largest Induced Suborders Satisfying the Chain Condition

For a fmite ordered set P, let c(P) denote the cardinality of the largest subset Q such that the induced suborder on Q satisfies the Jordan-Dedekind chain condition (JDCC), i.e., every maximal chain in Q has the same cardinality. For positive integers n, let be the minimum of c(P) over all ordered sets P of cardinahty n. We prove: &r 1 <f(n) < 4e AhfS (MOS) subject ckwiflcation (1980). 06AO5.

On the global asymptotic stability of difference equations satisfying a Markus-Yamabe condition

We prove a global asymptotic stability result for maps coming from n-th order difference equation and satisfying a Markus-Yamabe type condition. We also show that this result is sharp. 2000 Mathematics Subject Classification: Primary: 39A11. Secondary: 37C05, 37C75.