# [Ipopt] are block diagonal jacobians better for ma86?

Greg Horn gregmainland at gmail.com
Fri Mar 13 12:16:42 EDT 2015

```Hello,

I'm solving optimal control problems similar to

min           f(x1,x2..,xn,p)
x1..xn,p
s.t.
g1(x1,p) == 0
g2(x2,p) == 0
....
gn(xn,p) == 0

This gives a constraint jacobian with a dense column for variable p. I was
wondering if it would be more efficient to reformulate this to:

min                    f(x1,x2..,xn,p)
x1..xn,p,p1..pn
s.t.
g1(x1,p1) == 0
g2(x2,p2) == 0
....
gn(xn,pn) == 0
p - p1 == 0
p - p2 == 0
....
p - pn == 0

or

min                    f(x1,x2..,xn,p1)
x1..xn,p1..pn
s.t.
g1(x1,p1) == 0
g2(x2,p2) == 0
....
gn(xn,pn) == 0
p2 - p1 == 0
p3 - p2 == 0
....
pn - p{n-1} == 0

These would make a more block-diagonal jacobian. Does anyone know if the
sparse linear solvers solve these problems more efficiently? I usually use
HSL ma86.

Thanks!
Greg
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