Vertex Property applied on given polynomial function.
[valid,Bmin,Bvermin,zcap] = vertex(B,XB,N,ex1,zcap,LXsol,D1,Z1,Y)
Original Berstein Coefficient
Original Box(es)
Dimensional (Row) Matrix for all Variables in the Polynomial
Tolerence on the Bounds
Global Minimum Estimate
Temporary List for all minimzers at which Global minimum may lie
Total Number of Bernstein coefficients at vertices (Bvermin)
Total Number of Global Minimum Estimate (zcap)
New Bounds Calculated from Vertex Property
Indicates boxes feasible (valid=1) or boxes infeasible (valid=0)
Minimum Bernstein Coefficient Value
Vertex property plays vital role for finding out the global minimum.
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.