[Ipopt] Lagrange multipliers for inequality (<=) constraints

[Chunhua Men]

Thanks for your quick response - then I have to ask this question again:
why I got negative multipliers ( "lambda" in "finalize_solution") when all
my constraints are in the form of "<="?

Best, Chunhua

On Mon, Nov 7, 2016 at 7:15 AM, Stefan Vigerske <stefan at math.hu-berlin.de>
wrote:

> Hi,
>
> yes, internally, Ipopt creates your inequalities as equalities with slacks
> and ip_data is internal data, so refers to the internal representation of
> your problem.
> However, lambda refers to the problem with inequality constraints.
>
> Stefan
>
>
> On 11/07/2016 04:10 PM, Chunhua Men wrote:
>
>> Hi Stefan,
>>
>> Thanks for your response. I think I still miss something.... I have asked
>> a
>> question several months ago: all my constraints were inequality (<=) and I
>> wondered why I got negative "lambda" in "finalize_solution". Then I was
>> told that IPOPT treats all constraints as equalities with slacks...
>> However, in this email, I was told ip_data refer to the equality
>> constraints (+ slack variables), and "lambda" refer my
>> original inequalities (<=)?
>>
>> Thanks again, Chunhua
>>
>>
>>
>> On Mon, Nov 7, 2016 at 6:01 AM, Stefan Vigerske <stefan at math.hu-berlin.de
>> >
>> wrote:
>>
>> Hi,
>>>
>>> you should read lambda directly.
>>> ip_data should refer to the internal representation of your problem,
>>> where
>>> inequality constraints have been reformulated to equality constraints (+
>>> slack variables), so it might not be obvious what y_c() or y_d() mean.
>>> You can have a look at the documentation of intermediate_callback to get
>>> some idea how to bring y_c() and y_d() into the TNLP space:
>>> http://www.coin-or.org/Ipopt/documentation/node23.html#SECTI
>>> ON00053410000000000000
>>>
>>> Hope that helps,
>>> Stefan
>>>
>>>
>>> On 10/28/2016 12:44 AM, Chunhua Men wrote:
>>>
>>> Hello,
>>>>
>>>> I have a convex model with some inequality (<=)  nonlinear constraints.
>>>> At
>>>> the end of the optimization,  I wanted to get the Lagrange multipliers
>>>> for
>>>> each constraint. I found out there were 2 ways within
>>>> "finalize_solution(...)" to get them:
>>>> 1) read "lambda" directly;
>>>> 2) get from ip_data->curr()->y_d(). And I had to do some data transfer
>>>> to
>>>> get it -  and what I did was "static_cast<const
>>>> Ipopt::DenseVector*>(GetRawPtr(ip_data->curr()->y_c()))".
>>>>
>>>> However, these 2 methods could not give me the completely same results.
>>>> In
>>>> my case, there were 6 constraints: 3 of them were the same, and 3 of
>>>> them
>>>> were not.
>>>>
>>>> Did I do anything wrong? and what is the best way to get Lagrange
>>>> multipliers?  BTW, I am using " limited-memory" as
>>>> "hessian_approximation",
>>>> so I could not get Lagrange multipliers from "eval_h".
>>>>
>>>> Thanks! Chunhua
>>>>
>>>>
>>>>
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>>>>
>>>>
>>> --
>>> http://www.gams.com/~stefan
>>>
>>>
>>
>
> --
> http://www.gams.com/~stefan
>
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