Yemi,
As a follow-up, I coded your model and although the Interior-Point
algorithms in KNITRO cannot solve it, the Active-Set algorithm
(algorithm=3) solve it pretty easily (8 iterations). The output is at
the end of this message.
In general you should try all the KNITRO algorithms. KNITRO 8.0 has a
new multi-algorithm feature that will run all the KNITRO algorithms
(possibly in parallel) with the ability to terminate as soon as an
optimal solution is found. You can select this by setting
"KTR_PARAM_ALGORITHM=KTR_ALG_MULTI" (or "algorithm=5").
======================================
*** NO CHECK MADE FOR ZIENA LICENSE ***
KNITRO 8.0.0
Ziena Optimization
======================================
algorithm: 3
debug: 1
gradopt: 2
hessopt: 2
maxtime_cpu: 1e+08
maxtime_real: 1e+08
outlev: 4
outmode: 2
presolve: 0
KNITRO changing bar_switchrule from AUTO to 2.
KNITRO changing linsolver from AUTO to 4.
KNITRO performing finite-difference gradient computation with 1
thread.
Problem Characteristics
-----------------------
Objective goal: Minimize
Number of variables: 5
bounded below: 0
bounded above: 0
bounded below and above: 5
fixed: 0
free: 0
Number of constraints: 8
linear equalities: 0
nonlinear equalities: 5
linear inequalities: 0
nonlinear inequalities: 3
range: 3
Number of nonzeros in Jacobian: 40
Number of nonzeros in Hessian: 15
Iter fCount Objective FeasError OptError ||
Step|| CGits
-------- -------- -------------- ---------- ----------
---------- -------
0 6 2.785000e+01 6.756e+01
KNITRO performing finite-difference gradient computation with 1
thread.
1 12 2.050506e+01 3.986e+01 1.925e+01 2.236e
+00 1
2 18 1.261872e+01 8.700e+00 2.000e+01 3.289e
+00 1
3 24 9.791015e+00 1.902e+00 6.372e+00 1.379e
+00 1
4 30 8.719649e+00 2.869e-01 6.034e-01
5.356e-01 0
5 36 8.488260e+00 1.339e-02 1.866e-01
1.157e-01 0
6 42 8.476351e+00 3.545e-05 1.059e-02
5.954e-03 0
7 48 8.476319e+00 2.517e-10 2.836e-05
1.586e-05 1
8 54 8.476319e+00 2.220e-16 1.185e-07
1.126e-10 1
EXIT: Locally optimal solution found.
Final Statistics
----------------
Final objective value = 8.47631944665550e+00
Final feasibility error (abs / rel) = 2.22e-16 / 3.29e-18
Final optimality error (abs / rel) = 1.19e-07 / 3.95e-08
# of iterations = 8
# of CG iterations = 5
# of function evaluations = 54
# of gradient evaluations = 0
Total program time (secs) = 0.00471 ( 0.005 CPU
time)
Time spent in evaluations (secs) = 0.00002
===============================================================================
-Richard