Dear AMPL teams,

Sorry for your time. Currently im doing an experiment of “Outer active set method”, which means i have already had the jacobian of active constrains. Then the problem turns out to a QP problem with equality constraints. I call “Ipopt” solver to solve the problem, but it doesn’t work. In order to fix it, i have already regularized Hessian matrix “H_QP” and made the reduced Hessian matrix positive definite and it doesn’t work as the same. I’m thinking whether the bad initial point make the following error statements. Or can you give me some advice for how to test the QP problem feasible and debug it step by step.

This is Ipopt version 3.12.3, running with linear solver mumps.

NOTE: Other linear solvers might be more efficient (see Ipopt documentation).

Number of nonzeros in equality constraint Jacobian…: 4185

Number of nonzeros in inequality constraint Jacobian.: 0

Number of nonzeros in Lagrangian Hessian…: 3531

Total number of variables…: 1002

variables with only lower bounds: 0

variables with lower and upper bounds: 1002

variables with only upper bounds: 0

Total number of equality constraints…: 901

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

iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls

0 0.0000000e+000 2.37e-001 1.00e+002 -1.0 0.00e+000 - 0.00e+000 0.00e+000 0

WARNING: Problem in step computation; switching to emergency mode.

1r0.0000000e+000 2.37e-001 9.99e+002 -0.6 0.00e+000 20.0 0.00e+000 0.00e+000R 1

WARNING: Problem in step computation; switching to emergency mode.

Restoration phase is called at point that is almost feasible,

with constraint violation 0.000000e+000. Abort.

Restoration phase in the restoration phase failed.

Number of Iterations…: 1

(scaled) (unscaled)

Objective…: 0.0000000000000000e+000 0.0000000000000000e+000

Dual infeasibility…: 1.0000000000000000e+002 8.9585994490475059e+004

Constraint violation…: 2.3707976761747812e-001 2.3707976761747812e-001

Complementarity…: 1.0000000099999999e+001 8.9585995386334998e+003

Overall NLP error…: 1.0000000000000000e+002 8.9585994490475059e+004

Number of objective function evaluations = 2

Number of objective gradient evaluations = 2

Number of equality constraint evaluations = 2

Number of inequality constraint evaluations = 0

Number of equality constraint Jacobian evaluations = 2

Number of inequality constraint Jacobian evaluations = 0

Number of Lagrangian Hessian evaluations = 2

Total CPU secs in IPOPT (w/o function evaluations) = 0.085

Total CPU secs in NLP function evaluations = 0.000

EXIT: Restoration Failed!

solver : t_proc (avg) t_wall (avg) n_eval

nlp_f | 0 ( 0) 0 ( 0) 2

nlp_g | 0 ( 0) 0 ( 0) 2

nlp_grad_f | 0 ( 0) 0 ( 0) 3

nlp_hess_l | 0 ( 0) 0 ( 0) 1

nlp_jac_g | 0 ( 0) 0 ( 0) 3

total | 86.00ms ( 86.00ms) 86.59ms ( 86.59ms) 1

Thank you very much for your time and consideration.

Best regards,

Wang