[Ipopt] Bound on the objective function value

[Z. Caner Taskin]

Hi all,

I am using the C++ interface of Ipopt to solve a convex minimization 
problem. Specifically, the objective function is convex and all 
constraints are linear inequalities. I implemented the functions to 
provide first- and second-order derivatives, and Ipopt can usually solve 
my problem instances to optimality. However, sometimes it stops due to 
the limit on the number of iterations, and for such cases I need to 
calculate a lower bound on the objective function value. Since my 
problem is a convex optimization problem, the Lagrangian function should 
provide a strong dual for my problem. I verified that the value of the 
Lagrangian function is equal to the primal objective function value when 
the problem is solved optimally. However, I am having trouble getting 
consistent results for the  instances for which Ipopt stops due to the 
iteration limit (usually with relatively large dual infeasibility). I 
was wondering if anyone has experience obtaining bounds on the objective 
function value for convex problems?

Thanks in advance,

Caner

-- 
Z. Caner Taskin

PhD Candidate
Department of Industrial and Systems Engineering
University of Florida

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