testxxxx.pro

sqp程序包。用sqp算法实现非线性约束的优化求解

      1     7.151329e+00 
      2    -7.915196e+00 
      3    -7.500511e+00 
      4     5.782473e+00 
      5     3.404907e+00 
      6    -1.093693e+01 
      7    -2.181938e+01 
      8     3.871747e+00 
      9     9.419665e-01 

  multipliers: first estimate
  u =
    1   9.6873e-01    2   0.0000e+00    5   3.6504e+00    8  -4.1550e-01
    9  -8.1557e-01   11   2.5151e-02   12   0.0000e+00   14   2.6186e-01


  del=  5.88994e-02  b2n0=  5.54171e-04   b2n=  1.88800e-04   gfn=  2.59873e-03


 values of restrictions
 (   1    1.1477e-15    3.0000e+00)  (   2    1.0282e-02    2.9291e+00)  
 (   5    1.0282e-02    1.0000e+00)  (   8    5.6807e-02    1.0000e+00)  
 (   9    1.4350e-02    1.0000e+00)  (  11    5.7061e-02    1.0000e+00)  
 (  12    1.9707e-02    1.0000e+00)  (  14    5.0742e-04    1.0000e+00)  
 

   diag[r]=
  -1.0000e+00  -8.4403e-01  -8.5598e-01   4.6521e-02   4.4779e-02   3.7649e-02
   0.0000e+00   0.0000e+00


 gradient of restriction nr.   1
   1.0000e+00    1.0000e+00    1.0000e+00    1.0000e+00    1.0000e+00  
   1.0000e+00    1.0000e+00    1.0000e+00    1.0000e+00  
 

 gradient of restriction nr.   2
  -1.0000e+00   -1.0000e+00   -8.8000e-01   -1.0000e+00   -1.0000e+00  
  -9.6000e-01   -9.4000e-01   -1.0000e+00   -1.0000e+00  
 

 gradient of restriction nr.   5
   0.0000e+00    0.0000e+00    1.2000e-01    0.0000e+00    0.0000e+00  
   4.0000e-02    6.0000e-02    0.0000e+00    0.0000e+00  
 

 gradient of restriction nr.   8
   0.0000e+00    0.0000e+00    1.0000e+00    0.0000e+00    0.0000e+00  
   0.0000e+00    0.0000e+00    0.0000e+00    0.0000e+00  
 

 gradient of restriction nr.   9
   0.0000e+00    0.0000e+00    0.0000e+00    1.0000e+00    0.0000e+00  
   0.0000e+00    0.0000e+00    0.0000e+00    0.0000e+00  
 

 gradient of restriction nr.  11
   0.0000e+00    0.0000e+00    0.0000e+00    0.0000e+00    0.0000e+00  
   1.0000e+00    0.0000e+00    0.0000e+00    0.0000e+00  
 

 gradient of restriction nr.  12
   0.0000e+00    0.0000e+00    0.0000e+00    0.0000e+00    0.0000e+00  
   0.0000e+00    1.0000e+00    0.0000e+00    0.0000e+00  
 

 gradient of restriction nr.  14
   0.0000e+00    0.0000e+00    0.0000e+00    0.0000e+00    0.0000e+00  
   0.0000e+00    0.0000e+00    0.0000e+00    1.0000e+00  
 


 singular case : full regularized SQP
  del = 5.889944722528333e-02


  scalres=
   1.1123e+00   1.2000e+00   1.2000e+00   1.0000e+00   1.4000e+00   1.2000e+00
   1.2000e+00   1.2000e+00   1.2000e+00   1.2000e+00   1.2000e+00   1.2000e+00
   1.2000e+00   1.2000e+00   1.0000e+00   1.0000e+00   1.0000e+00   1.0000e+00
   1.0000e+00   1.0000e+00   1.0000e+00   1.0000e+00   1.0000e+00
gradients of binding constraints

 gradient of restriction nr.   1
   0.0000e+00  
   1.0000e+00    1.0000e+00    1.0000e+00    1.0000e+00    1.0000e+00  
   1.0000e+00    1.0000e+00    1.0000e+00    1.0000e+00  
 

 gradient of restriction nr.   2
   0.0000e+00  
  -1.0000e+00   -1.0000e+00   -8.8000e-01   -1.0000e+00   -1.0000e+00  
  -9.6000e-01   -9.4000e-01   -1.0000e+00   -1.0000e+00  
 

 gradient of restriction nr.   5
   0.0000e+00  
   0.0000e+00    0.0000e+00    1.2000e-01    0.0000e+00    0.0000e+00  
   4.0000e-02    6.0000e-02    0.0000e+00    0.0000e+00  
 

 gradient of restriction nr.   8
   0.0000e+00  
   0.0000e+00    0.0000e+00    1.0000e+00    0.0000e+00    0.0000e+00  
   0.0000e+00    0.0000e+00    0.0000e+00    0.0000e+00  
 

 gradient of restriction nr.   9
   0.0000e+00  
   0.0000e+00    0.0000e+00    0.0000e+00    1.0000e+00    0.0000e+00  
   0.0000e+00    0.0000e+00    0.0000e+00    0.0000e+00  
 

 gradient of restriction nr.  11
   0.0000e+00  
   0.0000e+00    0.0000e+00    0.0000e+00    0.0000e+00    0.0000e+00  
   1.0000e+00    0.0000e+00    0.0000e+00    0.0000e+00  
 

 gradient of restriction nr.  12
   0.0000e+00  
   0.0000e+00    0.0000e+00    0.0000e+00    0.0000e+00    0.0000e+00  
   0.0000e+00    1.0000e+00    0.0000e+00    0.0000e+00  
 

 gradient of restriction nr.  14
   0.0000e+00  
   0.0000e+00    0.0000e+00    0.0000e+00    0.0000e+00    0.0000e+00  
   0.0000e+00    0.0000e+00    0.0000e+00    1.0000e+00  
   condition number of r     -1.000000000000000e+00
  condition number of a     1.086621878985623e+03
additional increase of eta due to large clow


  current scaling,  scf =   1.1505e+03 clow =            4 eta =   2.8955e-20


  scalres=
   2.0785e+00   6.0000e-01   9.6000e-01   8.0000e-01   7.0000e-01   9.6000e-01
   9.6000e-01   6.0000e-01   6.0000e-01   9.6000e-01   6.0000e-01   6.0000e-01
   9.6000e-01   1.4768e+00   8.0000e-01   8.0000e-01   8.0000e-01   8.0000e-01
   8.0000e-01   8.0000e-01   8.0000e-01   8.0000e-01   8.0000e-01


  del=  5.88994e-02  b2n0=  5.54171e-04   b2n=  8.73803e-04   gfn=  2.59873e-03


 values of restrictions
 (   1    1.1477e-15    3.0000e+00)  (   2    1.0282e-02    2.9291e+00)  
 (   5    1.0282e-02    1.0000e+00)  (   8    5.6807e-02    1.0000e+00)  
 (   9    1.4350e-02    1.0000e+00)  (  11    5.7061e-02    1.0000e+00)  
 (  12    1.9707e-02    1.0000e+00)  (  14    5.0742e-04    1.0000e+00)  
 

 gradient of restriction nr.   1
   1.0000e+00    1.0000e+00    1.0000e+00    1.0000e+00    1.0000e+00  
   1.0000e+00    1.0000e+00    1.0000e+00    1.0000e+00  
 

 gradient of restriction nr.   2
  -1.0000e+00   -1.0000e+00   -8.8000e-01   -1.0000e+00   -1.0000e+00  
  -9.6000e-01   -9.4000e-01   -1.0000e+00   -1.0000e+00  
 

 gradient of restriction nr.   5
   0.0000e+00    0.0000e+00    1.2000e-01    0.0000e+00    0.0000e+00  
   4.0000e-02    6.0000e-02    0.0000e+00    0.0000e+00  
 

 gradient of restriction nr.   8
   0.0000e+00    0.0000e+00    1.0000e+00    0.0000e+00    0.0000e+00  
   0.0000e+00    0.0000e+00    0.0000e+00    0.0000e+00  
 

 gradient of restriction nr.   9
   0.0000e+00    0.0000e+00    0.0000e+00    1.0000e+00    0.0000e+00  
   0.0000e+00    0.0000e+00    0.0000e+00    0.0000e+00  
 

 gradient of restriction nr.  11
   0.0000e+00    0.0000e+00    0.0000e+00    0.0000e+00    0.0000e+00  
   1.0000e+00    0.0000e+00    0.0000e+00    0.0000e+00  
 

 gradient of restriction nr.  12
   0.0000e+00    0.0000e+00    0.0000e+00    0.0000e+00    0.0000e+00  
   0.0000e+00    1.0000e+00    0.0000e+00    0.0000e+00  
 

 gradient of restriction nr.  14
   0.0000e+00    0.0000e+00    0.0000e+00    0.0000e+00    0.0000e+00  
   0.0000e+00    0.0000e+00    0.0000e+00    1.0000e+00  
 exit from full SQP
            termination reason    1e+00
          final value of tauqp   1.000e+00
      sum norm of slack vector   0.000e+00


  phase=  0  scf0=  1.0000e+00
  d = 
  -2.5781e-02  -7.4328e-03   5.7687e-03   6.8957e-02  -2.1292e-02  -3.9272e-03
  -9.4897e-04  -1.4836e-02  -5.0742e-04

  multipliers: first estimate
  u =
    1   9.8926e-01    2   0.0000e+00    3   0.0000e+00    4   0.0000e+00
    5   0.0000e+00    6   0.0000e+00    7   0.0000e+00    8   0.0000e+00
    9   0.0000e+00   10   0.0000e+00   11   0.0000e+00   12   0.0000e+00
   13   0.0000e+00   14   6.8838e-01   15   0.0000e+00   16   0.0000e+00
   17   0.0000e+00   18   0.0000e+00   19   0.0000e+00   20   0.0000e+00
   21   0.0000e+00   22   0.0000e+00   23   0.0000e+00


  phase=  0  scf0=  1.0000e+00
  d =
  -2.5781e-02  -7.4328e-03   5.7687e-03   6.8957e-02  -2.1292e-02  -3.9272e-03
  -9.4897e-04  -1.4836e-02  -5.0742e-04


 start unimin

    phi=  4.8625e-01   dphi= -5.7163e-02    psi=  2.3856e-15 tau0/2=  5.0000e-01
     fx=  4.2264e-04  dscal=  1.0000e+00    scf=  1.1505e+03   upsi=  1.1477e-15
    sig=  1.0000e+00     fx=  3.9364e-04    psi=  2.1454e-16   upsi=  1.0322e-16


 end unimin

 sig=  1.0000e+00  num. f-evaluations 1
 list of inactive hit constraints
none
BFGS-update as in Pantoja and Mayne
  tk  =   6.198261e-03
 xsik =   0.000000e+00



================================================================================
            12-th iteration step
   scf=  1.1505e+03 psist=  2.0785e+00   psi=  2.1454e-16  upsi=  1.0322e-16
  fxst=  1.5154e-15    fx=  3.9364e-04
  x=
   3.1765e-01   5.7409e-02   6.2576e-02   8.3307e-02   2.2257e-01   5.3134e-02
   1.8758e-02   1.8460e-01   1.9949e-17
 valid permutation of x

  8   9   4   3   5   6   7   2   1 

         quasi-Newton-matrix full update

row/column        1              2              3              4      
      1     2.196254e+01   2.615943e-01   1.211583e-01  -7.607779e-01 
      2     0.000000e+00   3.078364e+01  -5.081317e+00   1.820164e+00 
      3     0.000000e+00   0.000000e+00   3.105094e+01  -4.390310e+00 
      4     0.000000e+00   0.000000e+00   0.000000e+00   3.336835e+00 
      5     0.000000e+00   0.000000e+00   0.000000e+00   0.000000e+00 
      6     0.000000e+00   0.000000e+00   0.000000e+00   0.000000e+00 
      7     0.000000e+00   0.000000e+00   0.000000e+00   0.000000e+00 
      8     0.000000e+00   0.000000e+00   0.000000e+00   0.000000e+00 
      9     0.000000e+00   0.000000e+00   0.000000e+00   0.000000e+00 

row/column        5              6              7              8      
      1    -1.927446e+01   8.847425e-01   4.960194e+00  -1.469379e+01 
      2    -2.346384e+00  -6.381472e+00  -7.258431e+00  -2.997400e+00 
      3    -2.094040e+00  -6.246784e+00  -7.129564e+00  -2.969087e+00 
      4     6.928625e+00  -1.562974e+00  -8.699388e-01  -6.491877e+00 
      5     2.048796e+01  -3.165403e+00   2.532316e+00  -2.414999e+01 
      6     0.000000e+00   2.940664e+01  -1.050976e+01  -6.746148e+00 
      7     0.000000e+00   0.000000e+00   2.532239e+01  -1.648449e+00 
      8     0.000000e+00   0.000000e+00   0.000000e+00   6.218885e+00 
      9     0.000000e+00   0.000000e+00   0.000000e+00   0.000000e+00 

row/column        9      
      1     7.117730e+00 
      2    -7.873250e+00 
      3    -7.500628e+00 
      4     4.684375e+00 
      5     3.676018e+00 
      6    -1.094509e+01 
      7    -2.189739e+01 
      8     4.183023e+00 
      9     9.418195e-01 

  multipliers: first estimate
  u =
    1  -4.5262e-02   14   7.7536e-01    2  -9.5890e-01


  del=  1.00000e-02  b2n0=  3.94413e-05   b2n=  6.17369e-04   gfn=  2.55495e-03


 values of restrictions
 (   1    1.0322e-16    3.0000e+00)  (  14    1.9949e-17    1.0000e+00)  
 (   2    1.0760e-02    2.9291e+00)  
 

   diag[r]=
  -1.0000e+00  -8.0805e-01  -5.7231e-03


 gradient of restriction nr.   1
   1.0000e+00    1.0000e+00    1.0000e+00    1.0000e+00    1.0000e+00  
   1.0000e+00    1.0000e+00    1.0000e+00    1.0000e+00  
 

 gradient of restriction nr.  14
   0.0000e+00    0.0000e+00    0.0000e+00    0.0000e+00    0.0000e+00  
   0.0000e+00    0.0000e+00    0.0000e+00    1.0000e+00  
 

 gradient of restriction nr.   2
  -1.0000e+00   -1.0000e+00   -8.8000e-01   -1.0000e+00   -1.0000e+00  
  -9.6000e-01   -9.4000e-01   -1.0000e+00   -1.0000e+00  
 
  multipliers: second estimate
  u =
    1  -4.5262e-02   14   7.7536e-01    2  -9.5890e-01
  condition number of r     1.747312531360756e+02
  condition number of a     1.086961408254853e+03


  current scaling,  scf =   1.1505e+03 clow =            4 eta =   2.8955e-20


  scalres=
   2.0785e+00   2.1178e+00   9.6000e-01   8.0000e-01   7.0000e-01   9.6000e-01
   9.6000e-01   6.0000e-01   6.0000e-01   9.6000e-01   6.0000e-01   6.0000e-01
   9.6000e-01   1.7507e+00   8.0000e-01   8.0000e-01   8.0000e-01   8.0000e-01
   8.0000e-01   8.0000e-01   8.0000e-01   8.0000e-01   8.0000e-01


  phase=  0  scf0=  1.0000e+00
  d =
  -2.9835e-01  -1.9887e-02   1.2284e-01   4.5012e-01  -2.1072e-01   2.5714e-02
   7.6320e-02  -1.4603e-01  -5.6552e-17


 start unimin

    phi=  4.5289e-01   dphi= -2.1540e-02    psi=  2.1454e-16 tau0/2=  5.0000e-01
     fx=  3.9364e-04  dscal=  1.0000e+00    scf=  1.1505e+03   upsi=  1.0322e-16
    sig=  1.0000e+00     fx=  1.3277e-03    psi=  1.7307e-16   upsi=  8.3267e-17
    sig=  5.0000e-01     fx=  6.2248e-04    psi=  1.1538e-16   upsi=  5.5511e-17
    sig=  1.2500e-01     fx=  4.0619e-04    psi=  1.4215e-16   upsi=  6.8392e-17
    sig=  1.2500e-02     fx=  3.9355e-04    psi=  3.2845e-16   upsi=  1.5802e-16


 end unimin

 sig=  1.2500e-02  num. f-evaluations 4
 list of inactive hit constraints
none
BFGS-update as in Pantoja and Mayne
  tk  =   3.793197e-01
 xsik =   0.000000e+00



================================================================================
            13-th iteration step
   scf=  1.1505e+03 psist=  2.0785e+00   psi=  3.2845e-16  upsi=  1.5802e-16
  fxst=  1.5154e-15    fx=  3.9355e-04
  x=
   3.1392