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non-linear programming - constraints

From: Dupuis
Subject: non-linear programming - constraints
Date: Fri, 11 Sep 2009 02:55:14 -0700 (PDT)


I'm trying to solve a non-linear minimisation problems where elements to
determine are part of a matrix: M = [a b; b c], with a and c >0. The
objective function requires that M be positive definite, i.e. ac - b^2 >=0.
I introduced an inequality constraint in sqp, yet during the search in
phi_L1, x sometimes is not acceptable with respect to the inequality
constraint. Is there a mean to strictly enforce the inequality constraint to
be valid ? Another way would be to take beff = sign(b)*(min(abs(b),
sqrt(a*c)) but I fear to introduce discontinuities in the inequality
function. Any hint ?

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