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sqp, objective and equality constraint gradients ?

From: Dupuis
Subject: sqp, objective and equality constraint gradients ?
Date: Thu, 10 Sep 2009 09:05:52 -0700 (PDT)

I have troubles getting sqp to work. Problem is defined as finding points on
an ellipse verifying some optimum condition.
objective: f =@(x) -prod(x);
gradient:  fg = @(x) -[x(2); x(1)];
equality: ce = @(x) (x-center).'*M*(x-center) - level
gradient: ceg = @(x) 2*M*(x-center)
where x is a (2, 1) vector, center is a (2, 1) vector with the center
coordinates, M is symetric, positive definite and level the sum of square of
the distances between each point and the two ellipse defining points.
The call is as follows:
1) find some good candidate by  trying a few points, let's call it xinit
2) lb = .95*xinit; ub = 1.05*xinit %# define a five percent search interval
3)  [xopt, obj, info, iter, nf, lambda] = sqp(xinit, {f fg}, {ce ceg}, [],
lb, ub);

The problems are at line 343 and 377
  F = feval (ce_grd, x);
  C = feval (ci_grd, x);
  A = [F; C];
F is supposed to be (n, 1); while C is (2*n, n): they are not compatible ...
I tried transposing F or padding F with zeroes : if line 343 succeeds, the
code fails elsewhere, f.i. in line 377:  t4 = norm (lambda .* con) which
expects lambda (rows(F), 1) and con (= [ce; ci]) to be the same dimensions.
 Could someone please tell me the expected dimensions of the various
gradients ?


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