Dear collegues,

I am interested by the following problem.

<< Consider a square interval matrix [A].

Denote by S the = set of=20 all A in [A] such that A is positive semi-definite

(i.e., A is = symmetric and=20 all its eigen values are >=3D0).

Find the smallest interval matrix = [B] which=20 contains S. >>

Denote by S the = set of=20 all A in [A] such that A is positive semi-definite

(i.e., A is = symmetric and=20 all its eigen values are >=3D0).

Find the smallest interval matrix = [B] which=20 contains S. >>

This problem is important for control applications or for global=20
optimization

(to build a non-convexity contractor, for = instance).

(to build a non-convexity contractor, for = instance).

With Didier Henrion, we have found (but maybe it was already known) =

that this problem is convex (because S is convex) and could = be

solved=20 efficiently by polynomial algorithms using an LMI

(linear matrix = inequality)=20 approach.

that this problem is convex (because S is convex) and could = be

solved=20 efficiently by polynomial algorithms using an LMI

(linear matrix = inequality)=20 approach.

My questions :

1) Could you please give me some references (if exist) on =
this=20
problem and

its possible applications,

2) Could I = find=20 somewhere an LMI solver which provides validated results.

its possible applications,

2) Could I = find=20 somewhere an LMI solver which provides validated results.

Thank you very much for your answers.

Regards,

Luc

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Luc=20 Jaulin

LISA, ISTIA, 62 avenue Notre Dame du Lac 49 000 Angers. =

T=E9l: 02 41=20 73 52 31 (=E0 l'UFR sciences) ou 02.41.22.65.78 (au LISA)

http://www.istia.univ-an= gers.fr/~jaulin

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