Necessary and sufficient condition on global optimality without convexity and second order differentiability

For a bilevel program with extremal value function, a necessary and sufficient condition for global optimality is given, which reduces the bilevel program to amax-minproblem with linked constraints. Also, for the case where the extremal value function is polyhedral, this optimality condition gives the possibility of a resolution via a maximization problem of a polyhedral convex function over a convex set. Finally, this case is completed by an algorithm.

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Consensus of Discrete Time Second-Order Multiagent Systems with Time Delay

Discrete Dynamics in Nature and Society ◽

10.1155/2012/390691 ◽

2012 ◽

Vol 2012 ◽

pp. 1-9 ◽

Cited By ~ 4

Author(s):

Wei Zhu

Keyword(s):

Time Delay ◽

Convergence Rate ◽

Theoretical Result ◽

Multiagent Systems ◽

Discrete Time ◽

Second Order ◽

Sufficient Condition ◽

Consensus Problem ◽

Necessary And Sufficient Condition ◽

Necessary And Sufficient

The consensus problem for discrete time second-order multiagent systems with time delay is studied. Some effective methods are presented to deal with consensus problems in discrete time multiagent systems. A necessary and sufficient condition is established to ensure consensus. The convergence rate for reaching consensus is also estimated. It is shown that arbitrary bounded time delay can safely be tolerated. An example is presented to illustrate the theoretical result.

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On Wiener's Criterion for an Elliptic Equation with Nonuniform Degeneration

Georgian Mathematical Journal ◽

10.1515/gmj.2007.607 ◽

2007 ◽

Vol 14 (4) ◽

pp. 607-626

Author(s):

Rabil A. Amanov ◽

Farman I. Mamedov

Keyword(s):

Elliptic Equation ◽

Laplace Equation ◽

Elliptic Equations ◽

Second Order ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Boundary Points ◽

Necessary And Sufficient

Abstract For some class of nonuniformly degenerated elliptic equations of second order, a necessary and sufficient condition for boundary points to be regular is found. This condition is an analogue of Wiener's criterion for the Laplace equation.

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Necessary and Sufficient Condition for the Existence of Solutions to a Discrete Second-Order Boundary Value Problem

Abstract and Applied Analysis ◽

10.1155/2012/951251 ◽

2012 ◽

Vol 2012 ◽

pp. 1-12 ◽

Cited By ~ 1

Author(s):

Chenghua Gao

Keyword(s):

Eigenvalue Problem ◽

Boundary Value Problem ◽

Existence Of Solutions ◽

Boundary Value ◽

Second Order ◽

Sufficient Condition ◽

First Eigenvalue ◽

Necessary And Sufficient Condition ◽

The First Eigenvalue ◽

Necessary And Sufficient

This paper is concerned with the existence of solutions for the discrete second-order boundary value problemΔ2u(t-1)+λ1u(t)+g(Δu(t))=f(t),t∈{1,2,…,T},u(0)=u(T+1)=0, whereT>1is an integer,f:{1,…,T}→R,g:R→Ris bounded and continuous, andλ1is the first eigenvalue of the eigenvalue problemΔ2u(t-1)+λu(t)=0,t∈T,u(0)=u(T+1)=0.

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Linear distribution processes

Journal of Applied Mathematics and Stochastic Analysis ◽

10.1155/s1048953398000045 ◽

1998 ◽

Vol 11 (1) ◽

pp. 43-58 ◽

Cited By ~ 3

Author(s):

L. Bel ◽

G. Oppenheim ◽

L. Robbiano ◽

M. C. Viano

Keyword(s):

Continuous Time ◽

Second Order ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Linear Distribution ◽

Stationary Increments ◽

Distribution Process ◽

Necessary And Sufficient

In this paper, we propose a generalization of continuous-time processed defined by Xt=∫f(t−s)dWs, to the case of f being a distribution. We give a necessary and sufficient condition for f, such that the obtained process is a second order distribution process. We study the moments and the regularity of these processes. In addition, we investigate a generalization to processes with stationary increments.

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