Warm Start example does not work as expected

[rakeshvar]

I am running the example given in the docs.
As I change the value of lambda the doc seems to imply that we get different results; but we do not.
What is the best way to solve this problem for different values of lambda?
using lambda=Variable(); fix!(lambda, 9)?

n = 9
y = 1:n
x = Variable(n)

lambda = 1
problem = minimize(sumsquares(y - x) + lambda * sumsquares(x - 10))
@time solve!(problem)
@show x.value  # Expected = 5.5:.5:9.5

lambda = 9
@time solve!(problem, warmstart=true)
@show x.value # Expected = 9.1:.1:9.9

[ericphanson]

Yes, I believe you should use fix!, and I made a pull request to change the docs to this effect; changing lambda as the docs suggest after the problem is constructed does not change the problem at all (in fact, since minimize is not a macro, I think it would be impossible for that to happen).

Note to use fix! you would need lambda = Variable(Positive()) because Convex does not update the sign automatically when using fix! (maybe this should be added?). You could also do

n = 9
y = 1:n
x = Variable(n)

lambda = 1
obj1 = sumsquares(y - x)
obj2 = sumsquares(x - 10)
problem = minimize( obj1 + lambda * obj2 )
@time solve!(problem, SCSSolver())
@show x.value  # Expected = 5.5:.5:9.5

lambda = 9
problem.objective =  obj1 + lambda * obj2 
@time solve!(problem, SCSSolver(),  warmstart=true)
@show x.value # Expected = 9.1:.1:9.9

which avoids fix!. Reusing obj1 and obj2, Convex doesn't have to recompute the conic forms, which might be helpful for large problems.