🚀 go-pugleaf

In article <1993Jan8.140544.25242@noao.edu> nroddier@noao.edu (Nicolas Roddier) writes:
>Hello control people!
>
>       I'm looking for some theorems that would garantee that an
>       optimization is an absolute minimum. E-L methods give some
>       necessary conditions for an optimzation to be an extremum.
>       How about some sufficient conditions for being the absolute
>       minimum.
>
>       Thanks for any help.
>
>       Nick.
>
>----------
>nroddier@noao.edu
>
If you try to find minimization in a bounded region, I recommend Branch and 
Bound method. This method has been introduced to calculate robust control 
problems recently. It is believed that the method can be used to solve 
non-convex optimization problems. Here are a few references:
 
R.R.E.de Gaston and M.G.Safonov, 1988, Exact calculation of the multiloop 
  stability margine, IEEE trans. AC-33, pp.156-171
A.Sederis and R.S.Sanches Pena, 1990, Robustness magin calculation with dynamic
  and real parametric uncertainty, IEEE trans AC-35, pp.970-974.
V.Balakrishnan, S.Boyd and S.Balemi, 1991, Branch and bound algorithm for 
  computing the minimum stability degree of parameter dependent linear systems,
  Int. J. Robust and Nonlinear Control. Vol.1, pp295-317.
M.P.Newlin and P.M.Young, 1992, Mixed mu problems and branch and bound 
  techniques, Proceedings of 31st CDC, pp.3175-3180

...and the references therein.
 
W.Wang