testxxxx.pro

sqp程序包。用sqp算法实现非线性约束的优化求解

             8-th iteration step
   scf=  1.0000e+00 psist=  5.5087e-01   psi=  7.4585e-16  upsi=  1.3540e-15
  fxst=  1.5154e-15    fx=  4.2691e-04
  x=
   3.3445e-01   6.7887e-02   5.8973e-02   1.2129e-02   2.3939e-01   6.0159e-02
   2.4375e-02   1.9652e-01   6.1181e-03
 valid permutation of x

  8   9   3   4   5   6   7   2   1 

         quasi-Newton-matrix full update

row/column        1              2              3              4      
      1     6.473424e-01   6.877412e-03   3.067490e-03  -1.750104e-02 
      2     0.000000e+00   9.082132e-01  -1.525698e-01   5.006414e-02 
      3     0.000000e+00   0.000000e+00   9.168180e-01  -1.206647e-01 
      4     0.000000e+00   0.000000e+00   0.000000e+00   1.511372e-01 
      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    -5.689637e-01   2.530860e-02   1.455564e-01  -4.337748e-01 
      2    -6.932851e-02  -1.878860e-01  -2.137187e-01  -8.842981e-02 
      3    -6.370546e-02  -1.852774e-01  -2.105696e-01  -8.932374e-02 
      4     1.541658e-01  -2.448999e-02  -1.104248e-02  -1.075649e-01 
      5     6.177735e-01  -1.021242e-01   6.569668e-02  -7.341738e-01 
      6     0.000000e+00   8.666009e-01  -3.093159e-01  -2.027803e-01 
      7     0.000000e+00   0.000000e+00   7.482193e-01  -5.268810e-02 
      8     0.000000e+00   0.000000e+00   0.000000e+00   1.541244e-01 
      9     0.000000e+00   0.000000e+00   0.000000e+00   0.000000e+00 

row/column        9      
      1     2.104251e-01 
      2    -2.320819e-01 
      3    -2.243202e-01 
      4     1.191954e-01 
      5     1.216446e-01 
      6    -3.261636e-01 
      7    -6.510965e-01 
      8     1.041097e-01 
      9     2.975792e-02 

  multipliers: first estimate
  u =
    1   6.2466e-04


  del=  9.22669e-04  b2n0=  1.77958e-02   b2n=  9.91010e-04   gfn=  2.61249e-03


 values of restrictions
 (   1    1.3540e-15    3.0000e+00)  
 

   diag[r]=
  -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  
 
  multipliers: second estimate
  u =
    1   6.2466e-04
  condition number of r     1.000000000000000e+00
  condition number of a     9.492070055885912e+02


  current scaling,  scf =   1.0000e+00 clow =            2 eta =   2.2273e-20


  scalres=
   5.5087e-01   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


  phase=  0  scf0=  1.0000e+00
  d =
   8.4822e-01  -2.6466e-01  -2.0467e-01   1.0320e-01   4.3441e-01  -2.7461e-01
  -4.2079e-01   2.8438e-01  -5.0546e-01


 start unimin

    phi=  4.2691e-04   dphi= -3.1669e-04    psi=  7.4585e-16 tau0/2=  5.0000e-01
     fx=  4.2691e-04  dscal=  1.0000e+00    scf=  1.0000e+00   upsi=  1.3540e-15
    sig=  1.2500e-01     fx=  4.7539e-04    psi=  1.4328e-01   upsi=  1.6554e-01
    sig=  1.5003e-02     fx=  4.2367e-04    psi=  8.0727e-04   upsi=  1.4655e-03
    sig=  1.5003e-03     fx=  4.2644e-04    psi=  6.6175e-16   upsi=  1.2013e-15


 end unimin

 sig=  1.5003e-03  num. f-evaluations 3
 list of inactive hit constraints
   2     2  
BFGS-update as in Pantoja and Mayne
  tk  =   5.000000e-01
 xsik =   0.000000e+00



================================================================================
             9-th iteration step
   scf=  1.0000e+00 psist=  5.5087e-01   psi=  6.6175e-16  upsi=  1.2013e-15
  fxst=  1.5154e-15    fx=  4.2644e-04
  x=
   3.3572e-01   6.7490e-02   5.8666e-02   1.2284e-02   2.4004e-01   5.9747e-02
   2.3744e-02   1.9695e-01   5.3598e-03
 valid permutation of x

  8   9   3   4   5   6   7   2   1 

         quasi-Newton-matrix full update

row/column        1              2              3              4      
      1     6.474572e-01   7.098375e-03   3.659339e-03  -1.710875e-02 
      2     0.000000e+00   9.082361e-01  -1.520685e-01   5.070148e-02 
      3     0.000000e+00   0.000000e+00   9.173970e-01  -1.201204e-01 
      4     0.000000e+00   0.000000e+00   0.000000e+00   1.488814e-01 
      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    -5.686683e-01   2.562783e-02   1.458386e-01  -4.334655e-01 
      2    -6.911741e-02  -1.877216e-01  -2.136105e-01  -8.820695e-02 
      3    -6.281769e-02  -1.844091e-01  -2.097712e-01  -8.844185e-02 
      4     1.619598e-01  -1.918771e-02  -5.438693e-03  -1.040364e-01 
      5     6.162240e-01  -1.025034e-01   6.540159e-02  -7.346497e-01 
      6     0.000000e+00   8.670565e-01  -3.083008e-01  -2.016015e-01 
      7     0.000000e+00   0.000000e+00   7.490741e-01  -5.053003e-02 
      8     0.000000e+00   0.000000e+00   0.000000e+00   1.584361e-01 
      9     0.000000e+00   0.000000e+00   0.000000e+00   0.000000e+00 

row/column        9      
      1     2.106679e-01 
      2    -2.320306e-01 
      3    -2.235852e-01 
      4     1.269745e-01 
      5     1.191725e-01 
      6    -3.261942e-01 
      7    -6.498837e-01 
      8     1.074783e-01 
      9     2.836991e-02 

  multipliers: first estimate
  u =
    1   5.8271e-03    2   4.9688e-03


  del=  3.98532e-03  b2n0=  1.87147e-02   b2n=  9.91901e-04   gfn=  2.61084e-03


 values of restrictions
 (   1    1.2013e-15    3.0000e+00)  (   2    1.0854e-02    2.9291e+00)  
 

   diag[r]=
  -1.0000e+00  -1.0251e-01


 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  
 
  multipliers: second estimate
  u =
    1   5.8271e-03    2   4.9688e-03
  condition number of r     9.755564861428841e+00
  condition number of a     1.045679655949844e+03


  current scaling,  scf =   1.0000e+00 clow =            2 eta =   2.2273e-20


  scalres=
   5.5087e-01   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


  phase=  0  scf0=  1.0000e+00
  d =
   1.4016e-01  -5.3122e-02  -3.3961e-02   6.0902e-02   6.6876e-02  -5.2780e-02
  -7.7798e-02   4.3237e-02  -9.3515e-02


 start unimin

    phi=  4.2644e-04   dphi= -8.8862e-05    psi=  6.6175e-16 tau0/2=  5.0000e-01
     fx=  4.2644e-04  dscal=  1.0000e+00    scf=  1.0000e+00   upsi=  1.2013e-15
    sig=  1.0000e+00     fx=  4.9259e-04    psi=  2.4510e-01   upsi=  2.8118e-01
    sig=  5.0000e-01     fx=  4.4166e-04    psi=  9.1413e-02   upsi=  1.0677e-01
    sig=  1.2500e-01     fx=  4.2192e-04    psi=  3.4868e-03   upsi=  6.3296e-03
    sig=  1.2500e-02     fx=  4.2533e-04    psi=  6.1971e-16   upsi=  1.1250e-15


 end unimin

 sig=  1.2500e-02  num. f-evaluations 4
 list of inactive hit constraints
none
BFGS-update as in Pantoja and Mayne
  tk  =   5.125507e-02
 xsik =   0.000000e+00



================================================================================
            10-th iteration step
   scf=  1.1505e+03 psist=  6.3378e+02   psi=  7.1298e-13  upsi=  1.1250e-15
  fxst=  1.5154e-15    fx=  4.2533e-04
  x=
   3.3747e-01   6.6826e-02   5.8242e-02   1.3045e-02   2.4088e-01   5.9087e-02
   2.2771e-02   1.9749e-01   4.1908e-03
 valid permutation of x

  8   9   3   4   5   6   7   2   1 

         quasi-Newton-matrix full update

row/column        1              2              3              4      
      1     2.196756e+01   2.619237e-01   1.264554e-01  -6.473725e-01 
      2     0.000000e+00   3.079868e+01  -5.074106e+00   1.784684e+00 
      3     0.000000e+00   0.000000e+00   3.104891e+01  -4.373700e+00 
      4     0.000000e+00   0.000000e+00   0.000000e+00   3.864220e+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    -1.926564e+01   8.851778e-01   4.959574e+00  -1.468321e+01 
      2    -2.330998e+00  -6.354195e+00  -7.226415e+00  -2.981706e+00 
      3    -2.083131e+00  -6.239902e+00  -7.121587e+00  -2.959046e+00 
      4     6.801370e+00  -1.581474e+00  -1.236482e+00  -4.982669e+00 
      5     2.054739e+01  -3.130520e+00   2.672418e+00  -2.458352e+01 
      6     0.000000e+00   2.942654e+01  -1.047064e+01  -6.661039e+00 
      7     0.000000e+00   0.000000e+00   2.533659e+01  -1.417109e+00 
      8     0.000000e+00   0.000000e+00   0.000000e+00   6.122427e+00 
      9     0.000000e+00   0.000000e+00   0.000000e+00   0.000000e+00 

row/column        9      
      1     7.165609e+00 
      2    -7.896078e+00 
      3    -7.491309e+00 
      4     6.012742e+00 
      5     3.312604e+00 
      6    -1.092166e+01 
      7    -2.173943e+01 
      8     4.195069e+00 
      9     9.226030e-01 

  multipliers: first estimate
  u =
    1   4.5614e-01


  del=  3.62282e-03  b2n0=  5.40780e-04   b2n=  1.51157e-03   gfn=  2.60753e-03


 values of restrictions
 (   1    1.1250e-15    3.0000e+00)  
 

   diag[r]=
  -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  
 
  multipliers: second estimate
  u =
    1   4.5614e-01
  condition number of r     1.000000000000000e+00
  condition number of a     1.132564463881875e+03


  current scaling,  scf =   1.1505e+03 clow =            3 eta =   2.2273e-20


  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


  phase=  0  scf0=  1.0000e+00
  d =
   7.4326e-01  -2.4763e-01  -1.7898e-01   1.6275e-01   3.7245e-01  -2.5282e-01
  -3.8231e-01   2.4289e-01  -4.5962e-01


 start unimin

    phi=  4.8935e-01   dphi= -3.8710e-01    psi=  1.2513e-15 tau0/2=  5.0000e-01
     fx=  4.2533e-04  dscal=  1.0000e+00    scf=  1.1505e+03   upsi=  1.1250e-15
    sig=  1.2500e-01     fx=  4.6396e-04    psi=  1.7452e-01   upsi=  1.5115e-01
    sig=  1.6028e-02     fx=  4.2318e-04    psi=  3.5326e-03   upsi=  3.1760e-03
    sig=  8.0141e-03     fx=  4.2264e-04    psi=  1.2766e-15   upsi=  1.1477e-15


 end unimin

 sig=  8.0141e-03  num. f-evaluations 3
 list of inactive hit constraints
   2     2  
BFGS-update as in Pantoja and Mayne
  tk  =   5.000000e-01
 xsik =   0.000000e+00



================================================================================
            11-th iteration step
   scf=  1.1505e+03 psist=  1.1123e+00   psi=  1.2766e-15  upsi=  1.1477e-15
  fxst=  1.5154e-15    fx=  4.2264e-04
  x=
   3.4343e-01   6.4842e-02   5.6807e-02   1.4350e-02   2.4386e-01   5.7061e-02
   1.9707e-02   1.9943e-01   5.0742e-04
 valid permutation of x

  8   9   3   4   5   6   7   2   1 

         quasi-Newton-matrix full update

row/column        1              2              3              4      
      1     2.196330e+01   2.458264e-01   1.240329e-01  -6.579921e-01 
      2     0.000000e+00   3.078849e+01  -5.081937e+00   1.777258e+00 
      3     0.000000e+00   0.000000e+00   3.105094e+01  -4.391902e+00 
      4     0.000000e+00   0.000000e+00   0.000000e+00   3.945096e+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    -1.928186e+01   8.728147e-01   4.946428e+00  -1.469826e+01 
      2    -2.357903e+00  -6.372659e+00  -7.244745e+00  -3.006081e+00 
      3    -2.093631e+00  -6.246620e+00  -7.129444e+00  -2.968794e+00 
      4     6.537055e+00  -1.673367e+00  -1.325174e+00  -4.997159e+00 
      5     2.060428e+01  -3.157709e+00   2.631301e+00  -2.462827e+01 
      6     0.000000e+00   2.940661e+01  -1.051342e+01  -6.738507e+00 
      7     0.000000e+00   0.000000e+00   2.530377e+01  -1.550643e+00 
      8     0.000000e+00   0.000000e+00   0.000000e+00   5.717033e+00 
      9     0.000000e+00   0.000000e+00   0.000000e+00   0.000000e+00 

row/column        9