Warm-starting bound multipliers

[dpo]

I’m a little confused as to how to warm start the multipliers associated with bound constraints. The documentation states that the only two accepted values for bound_mult_init_method are constant and mu-based. Why then does get_starting_point() request $z_L$ and $z_U$? If I set $z_L$ and $z_U$ to specific (positive) values, I don’t see any difference in the initial dual feasibility compared to when I just set them to ones. Could you please explain what options are relevant here and how to set $z_L$ and $z_U$?

Thank you!

[svigerske]

get_starting_point() should request values for z_L and z_U only if option warm_start_init_point has been enabled. bound_mult_init_method should only matter if warm_start_init_point is off, and then does not care about values in z_L and z_U.

[dpo]

Ok, thank you. My situation is that I have fixed variables that I want to manage myself (instead of IPOPT eliminating them). The fixed variables are indicated by identical lower and upper bounds. I’m trying to provide a good initial estimate of the multipliers for those fixed variables by setting $z_L$ to the opposite of the negative part, and $z_U$ to the positive part. Is that the right way to do it with IPOPT? I’m a bit confused because the initial dual feasibility reported by IPOPT is the same whether I warm start the multipliers or not.

[svigerske]

So you set option fixed_variable_treatment to make_constraint? It looks like in this case, the warm-start values for z_L and z_U are ignored by Ipopt and instead 0 is used:

Ipopt/src/Interfaces/IpTNLPAdapter.cpp

Lines 1618 to 1623 in a8e153f

	if( fixed_variable_treatment_ == MAKE_CONSTRAINT )
	{
	// ToDo maybe use info from z_L and Z_U here?
	const Number zero = 0.;
	IpBlasCopy(n_x_fixed_, &zero, 0, &values[P_c_g_->NCols()], 1);
	}

If you are in this case, then it may be worth to do this todo.

[dpo]

Yes, I set fixed_variable_treatment = make_constraint. The code you point to explains the behavior I’m observing. Are you seeing clearly how it should be modified to use info from $z_L$ and $z_U$? Would that be a large change?

[svigerske]

Sorry for the delay. I hope this is fixed now on stable/3.14 (change 363143b).