Name

vertex — Vertex Property applied on given polynomial function.

Calling Sequence

   [valid,Bmin,Bvermin,zcap] = vertex(B,XB,N,ex1,zcap,LXsol,D1,Z1,Y)
   
   

Parameters

B :

Original Berstein Coefficient

XB:

Original Box(es)

N :

Dimensional (Row) Matrix for all Variables in the Polynomial

ex1:

Tolerence on the Bounds

zcap:

Global Minimum Estimate

LXsol:

Temporary List for all minimzers at which Global minimum may lie

D1:

Total Number of Bernstein coefficients at vertices (Bvermin)

Z1:

Total Number of Global Minimum Estimate (zcap)

Y :

New Bounds Calculated from Vertex Property

valid :

Indicates boxes feasible (valid=1) or boxes infeasible (valid=0)

Bmin :

Minimum Bernstein Coefficient Value

Description

Vertex property plays vital role for finding out the global minimum.

Examples

// Vertex Property applied on given polynomial function
[valid,Bmin,Bvermin,zcap] = vertex(B,XB,N,ex1,zcap,LXsol,D1,Z1,Y)
// Function calculates estimate minimum position and compares with vertices value.

   

See also

store, getverind, sun2lin, ind2x, lin2sub

Authors

Mr. Dhiraj B. Magare
IDP in Systems and Control Engineering
Indian Institute of Technology Bombay
Mr. Bhagyesh V. Patil
IDP in Systems and Control Engineering
Indian Institute of Technology Bombay
Prof. P.S.V. Nataraj
IDP in Systems and Control Engineering
Indian Institute of Technology Bombay

Bibliography

1. Shashwati Ray, P.S.V. Nataraj. An efficient algorithm for range computation of polynomials using the Bernstein form. Journal of Global Optimization, 45: 403-426,2009;

2. G. T. Cargo and O. Shisha. The Bernstein form of a polynomial. Jl. of research of NBS,70B:79-81,1966.

3. S. Ray, A new approach to range computation of polynomial problems using the Bernstein form. PhD thesis, Systems and Control Engineering, IIT Bombay, India, 2007.