[Ipopt] why can iteration 1-2-3 get worsen?

[Xiaoming Yu]

Hi Andreas :

I used IPOPT 3.3.4 and had results as below. My initial design (iter=0)
is a feasible design. However, iter 1, 2, and 3 get some worsen not
better (objective increases). Why that happens?

Is that my due to automatic scaling?

1) My design variables (all total =301501 in range 0.001, 1.0). Do you
think I need to scale the design variables to 1.0 for all variables?
SDi= 1.0/xi? Any comments? 

2) If small obj < 1.0-2  or very small gradients (like 1.-5 to 1.-10),
use your default parameter, the results are not quite good sometime. I
guess Sometimes, I set my own scaling factor :

SCFOBJ = 1.0D+5/abs(OBJ)
IERR=IPADDNUMOPTION(IPROBLEM,'obj_scaling_factor',SCFOBJ)

Optimization results are much better (may be due to increases gradients
in orders?). If I set 'obj_scaling_factor, SCFOBJ', Does the IPOPT
automatic scaling function still perform based on my already scaled
"SCFOBJ"?

Why is best way to deal with very small gradients?

Thanks,

Xiaoming

Number of nonzeros in equality constraint Jacobian...:        0
Number of nonzeros in inequality constraint Jacobian.:   301501
Number of nonzeros in Lagrangian Hessian.............:        0

Total number of variables............................:   301501
                     variables with only lower bounds:        0
                variables with lower and upper bounds:   301501
                     variables with only upper bounds:        0
Total number of equality constraints.................:        0
Total number of inequality constraints...............:        1
        inequality constraints with only lower bounds:        0
   inequality constraints with lower and upper bounds:        0
        inequality constraints with only upper bounds:        1

iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du
alpha_pr  ls
   0  8.6609746e+03 8.13e-03 3.92e+00   0.0 0.00e+00    -  0.00e+00
0.00e+00   0
   1  8.7928926e+03 6.71e-07 9.92e-02  -2.2 8.78e-03    -  9.74e-01
1.00e+00f  1
   2  8.7842295e+03 4.99e-07 6.57e-02  -2.8 6.36e-02    -  1.00e-00
1.00e+00f  1
   3  8.6665713e+03 5.90e-07 7.30e-02  -3.4 6.96e-02    -  9.91e-01
1.00e+00f  1
   4  8.6328262e+03 1.03e-06 5.93e-02  -4.0 5.79e-02    -  9.99e-01
4.58e-01f  1
   5  8.6325098e+03 2.42e-07 5.32e-02  -4.6 5.32e-02    -  1.00e+00
5.57e-03f  1