Access the complementarity infeasibility, dual infeasibility, and the primal infeasibility

how can I access the complementarity infeasibility, the dual infeasibility, and primal infeasibility after optimizing with Ipopt? Do I need to use a callback function for this or does IPOPT have a function for this?

Your other answer is correct; you can access the primal and dual infeasibility using a solver-specific callback:

https://github.com/jump-dev/Ipopt.jl#solver-specific-callback

<s>There is no support for accessing the complementarity infeasibility.</s>

Ipopt.jl v1.2.0 adds support for this:

julia> using JuMP

julia> import Ipopt

julia> model = Model(Ipopt.Optimizer)
A JuMP Model
Feasibility problem with:
Variables: 0
Model mode: AUTOMATIC
CachingOptimizer state: EMPTY_OPTIMIZER
Solver name: Ipopt

julia> @variable(model, 0 <= x <= π)
x

julia> @NLobjective(model, Min, (x - cos(x))^2)

julia> function my_callback(
           alg_mod::Cint,
           iter_count::Cint,
           obj_value::Float64,
           inf_pr::Float64,
           inf_du::Float64,
           mu::Float64,
           d_norm::Float64,
           regularization_size::Float64,
           alpha_du::Float64,
           alpha_pr::Float64,
           ls_trials::Cint,
        )
           m, n = 0, 1
           x, z_L, z_U = zeros(n), zeros(n), zeros(n)
           g, lambda = zeros(m), zeros(m)
           scaled = false
           prob = unsafe_backend(model).inner
           Ipopt.GetIpoptCurrentIterate(prob, scaled, n, x, z_L, z_U, m, g, lambda)
           x_L_violation, x_U_violation = zeros(n), zeros(n)
           compl_x_L, compl_x_U, grad_lag_x = zeros(n), zeros(n), zeros(n)
           nlp_constraint_violation, compl_g = zeros(m), zeros(m)
           Ipopt.GetIpoptCurrentViolations(
               prob,
               scaled,
               n,
               x_L_violation,
               x_U_violation,
               compl_x_L,
               compl_x_U,
               grad_lag_x,
               m,
               nlp_constraint_violation,
               compl_g,
           )
           @show x
           @show z_L
           @show z_U
           @show x_L_violation
           @show x_U_violation
           @show compl_x_L
           @show compl_x_U
           @show grad_lag_x
           return false
       end
my_callback (generic function with 1 method)

julia> MOI.set(model, Ipopt.CallbackFunction(), my_callback)

julia> optimize!(model)
This is Ipopt version 3.14.4, running with linear solver MUMPS 5.4.1.

Number of nonzeros in equality constraint Jacobian...:        0
Number of nonzeros in inequality constraint Jacobian.:        0
Number of nonzeros in Lagrangian Hessian.............:        1

Total number of variables............................:        1
                     variables with only lower bounds:        0
                variables with lower and upper bounds:        1
                     variables with only upper bounds:        0
Total number of equality constraints.................:        0
Total number of inequality constraints...............:        0
        inequality constraints with only lower bounds:        0
   inequality constraints with lower and upper bounds:        0
        inequality constraints with only upper bounds:        0

x = [0.00999999]
z_L = [1.0]
z_U = [1.0]
x_L_violation = [0.0]
x_U_violation = [0.0]
compl_x_L = [0.01]
compl_x_U = [3.13159269500572]
grad_lag_x = [-1.999698671463963]
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
   0  9.8000102e-01 0.00e+00 2.00e+00  -1.0 0.00e+00    -  0.00e+00 0.00e+00   0

Number of Iterations....: 0

                                   (scaled)                 (unscaled)
Objective...............:   9.8000102332194250e-01    9.8000102332194250e-01
Dual infeasibility......:   1.9996986714639631e+00    1.9996986714639631e+00
Constraint violation....:   0.0000000000000000e+00    0.0000000000000000e+00
Variable bound violation:   0.0000000000000000e+00    0.0000000000000000e+00
Complementarity.........:   3.1315926950057200e+00    3.1315926950057200e+00
Overall NLP error.......:   3.1315926950057200e+00    3.1315926950057200e+00


Number of objective function evaluations             = 1
Number of objective gradient evaluations             = 1
Number of equality constraint evaluations            = 0
Number of inequality constraint evaluations          = 0
Number of equality constraint Jacobian evaluations   = 0
Number of inequality constraint Jacobian evaluations = 0
Number of Lagrangian Hessian evaluations             = 0
Total seconds in IPOPT                               = 0.064

EXIT: Stopping optimization at current point as requested by user.

See the Ipopt documentation for details:

• https://coin-or.github.io/Ipopt/IpStdCInterface_8h.html#acf68350650b7a893061e110ab0e9264f
• https://coin-or.github.io/Ipopt/IpStdCInterface_8h.html#ae505cff0e907b9049062f665dadd8be9

Looks like I can get primal infeasibility (inf_pr) and dual infeasibility (inf_du) from this function,

 function my_callback(
alg_mod::Cint,
iter_count::Cint,
obj_value::Float64,
inf_pr::Float64,
inf_du::Float64,
mu::Float64,
d_norm::Float64,
regularization_size::Float64,
alpha_du::Float64,
alpha_pr::Float64,
ls_trials::Cint)
return true
end

but what about complementarity infeasibility?