undefexa.pro~orig

sqp程序包。用sqp算法实现非线性约束的优化求解

  1   2 

  multipliers: first estimate
  u =
    1   9.3813e+00    2   0.0000e+00


  del=  5.52313e-02  b2n0=  0.00000e+00   b2n=  0.00000e+00   gfn=  1.20667e+01


 values of restrictions
 (   1   -4.5676e-04    1.2863e+00)  (   2    1.3196e-01    2.3893e+00)  
 

   diag[r]=
  -1.0000e+00   5.4131e-01

  multipliers: second estimate
  u =
    1   9.3813e+00    2   0.0000e+00
  condition number of r     1.847377108838539e+00
  condition number of a     1.000000000000000e+00
additional increase of eta due to large clow


  current scaling,  scf =   1.0000e+00 clow =            2 eta =   1.5080e-02


  scalres=
   1.8966e+01   1.3500e+00   1.0000e+00   1.0000e+00


  phase=  2  scf0=  1.0000e+00
  d =
  -5.4205e-02   8.5793e-02


  dd=
   9.1225e-03  -7.5959e-03


 start unimin

    phi= -3.1108e+00   dphi= -4.3782e-03    psi=  8.6632e-03 tau0/2=  5.0000e-01
     fx= -3.1195e+00  dscal=  1.0000e+00    scf=  1.0000e+00   upsi=  4.5676e-04
    sig=  1.0000e+00     fx= -3.1047e+00    psi=  0.0000e+00   upsi=  0.0000e+00
    sig=  5.0000e-01     fx= -3.1160e+00    psi=  1.5821e-03   upsi=  8.3415e-05


 end unimin

 sig=  5.0000e-01  num. f-evaluations 2
 list of inactive hit constraints
none
BFGS-update as in Pantoja and Mayne
  tk  =   1.029860e-02
 xsik =   0.000000e+00



================================================================================
             7-th iteration step
   scf=  1.0000e+00 psist=  0.0000e+00   psi=  1.5821e-03  upsi=  8.3415e-05
  fxst= -2.0000e+00    fx= -3.1160e+00
  x=
   6.6601e-01   1.1260e+00
 valid permutation of x

  1   2 

  multipliers: first estimate
  u =
    1   9.3521e+00    2   8.1010e-16


  del=  6.33352e-02  b2n0=  4.75529e-13   b2n=  5.22183e-15   gfn=  1.22345e+01


 values of restrictions
 (   1   -8.3415e-05    1.3082e+00)  (   2    6.6142e-02    2.4640e+00)  
 

   diag[r]=
  -1.0000e+00   9.9965e-01

  multipliers: second estimate
  u =
    1   9.3521e+00    2   8.1010e-16
  condition number of r     1.000351765612208e+00
  condition number of a     7.183985411777938e+06


  current scaling,  scf =   1.0000e+00 clow =            2 eta =   1.5080e-02


  scalres=
   1.8966e+01   1.3500e+00   1.0000e+00   1.0000e+00


  phase=  2  scf0=  1.0000e+00
  d =
  -2.3460e-02   3.9788e-02


  dd=
   1.6882e-03  -1.4526e-03


 start unimin

    phi= -3.1144e+00   dphi= -8.0199e-04    psi=  1.5821e-03 tau0/2=  5.0000e-01
     fx= -3.1160e+00  dscal=  1.0000e+00    scf=  1.0000e+00   upsi=  8.3415e-05
    sig=  1.0000e+00     fx= -3.1143e+00    psi=  0.0000e+00   upsi=  0.0000e+00
    sig=  5.0000e-01     fx= -3.1155e+00    psi=  5.5392e-04   upsi=  2.9205e-05


 end unimin

 sig=  5.0000e-01  num. f-evaluations 2
 list of inactive hit constraints
none
BFGS-update as in Pantoja and Mayne
  tk  =   2.133458e-03
 xsik =   0.000000e+00



================================================================================
             8-th iteration step
   scf=  1.0000e+00 psist=  0.0000e+00   psi=  5.5392e-04  upsi=  2.9205e-05
  fxst= -2.0000e+00    fx= -3.1155e+00
  x=
   6.5470e-01   1.1455e+00
 valid permutation of x

  1   2 

  multipliers: first estimate
  u =
    1   9.3479e+00    2   1.8000e-16


  del=  2.46251e-02  b2n0=  1.84033e-13   b2n=  4.83742e-15   gfn=  1.23337e+01


 values of restrictions
 (   1   -2.9205e-05    1.3194e+00)  (   2    3.3085e-02    2.4998e+00)  
 

   diag[r]=
  -1.0000e+00   9.9924e-01

  multipliers: second estimate
  u =
    1   9.3479e+00    2   1.8000e-16
  condition number of r     1.000759386979650e+00
  condition number of a     1.179704620233416e+07


  current scaling,  scf =   1.0000e+00 clow =            2 eta =   1.5080e-02


  scalres=
   1.8966e+01   1.3500e+00   1.0000e+00   1.0000e+00


  phase=  2  scf0=  1.0000e+00
  d =
  -1.0963e-02   1.9226e-02


  dd=
   3.6802e-04  -3.2198e-04


 start unimin

    phi= -3.1149e+00   dphi= -2.8091e-04    psi=  5.5392e-04 tau0/2=  5.0000e-01
     fx= -3.1155e+00  dscal=  1.0000e+00    scf=  1.0000e+00   upsi=  2.9205e-05
    sig=  1.0000e+00     fx= -3.1151e+00    psi=  0.0000e+00   upsi=  0.0000e+00


 end unimin

 sig=  1.0000e+00  num. f-evaluations 1
 list of inactive hit constraints
none
BFGS-update as in Pantoja and Mayne
  tk  =   4.898331e-04
 xsik =   0.000000e+00



================================================================================
             9-th iteration step
   scf=  1.0000e+00 psist=  0.0000e+00   psi=  0.0000e+00  upsi=  0.0000e+00
  fxst= -2.0000e+00    fx= -3.1151e+00
  x=
   6.4410e-01   1.1644e+00
 valid permutation of x

  1   2 

  multipliers: first estimate
  u =
    2   3.9088e-05


  del=  9.47300e-02  b2n0=  2.12985e+00   b2n=  1.24352e+01   gfn=  1.24351e+01


 values of restrictions
 (   2    1.2277e-05    2.5345e+00)  (   1    1.0487e-05    1.3307e+00)  
 

   diag[r]=
   1.0000e+00   9.9956e-01

  multipliers: second estimate
  u =
    2   2.2835e-16    1   9.3448e+00
  condition number of r     1.000435640897857e+00
  condition number of a     2.141932316396262e+07


  current scaling,  scf =   1.0000e+00 clow =            2 eta =   1.5080e-02


  scalres=
   1.8966e+01   1.3500e+00   1.0000e+00   1.0000e+00


  phase=  2  scf0=  1.0000e+00
  d =
  -1.5636e-05   1.1986e-05


  dd=
   2.5584e-10  -1.7155e-10


 start unimin

    phi= -3.1151e+00   dphi= -9.7999e-05    psi=  0.0000e+00 tau0/2=  5.0000e-01
     fx= -3.1151e+00  dscal=  1.0000e+00    scf=  1.0000e+00   upsi=  0.0000e+00
    sig=  1.0000e+00     fx= -3.1152e+00    psi=  0.0000e+00   upsi=  0.0000e+00
    sig=  2.0000e+00     fx= -3.1153e+00    psi=  2.1548e-04   upsi=  2.2764e-05


 end unimin

 sig=  1.0000e+00  num. f-evaluations 2
 list of inactive hit constraints
none
restart with scaled unit matrix
restart with scaled unit matrix



================================================================================
            10-th iteration step
   scf=  1.0000e+00 psist=  0.0000e+00   psi=  0.0000e+00  upsi=  0.0000e+00
  fxst= -2.0000e+00    fx= -3.1152e+00
  x=
   6.4409e-01   1.1644e+00
 valid permutation of x

  2   1 

  multipliers: first estimate
  u =
    1   9.3456e+00    2  -1.0613e-15

     n=         2    nh=         0    ng=         4

  epsx= 1.000e-10 sigsm= 1.490e-08

startvalue
  1.0000000e+00   1.0000000e+00 

  eps=  2.22e-16  tol= 1.98e-323 del0=  1.00e+00 delm=  1.00e-06 tau0=  1.00e+00
  tau=  1.00e-01   sd=  1.00e-01   sw=  3.67e-11  rho=  1.00e-06 rho1=  1.00e-10
 scfm=  1.00e+04  c1d=  1.00e-02 epdi=  1.00e-08
  nre=         4 anal=         1

 termination reason:
 KT-conditions satisfied, no further correction computed
 evaluations of f                           24
 evaluations of grad f                      10
 evaluations of constraints                 60
 evaluations of grads of constraints        18
 final scaling of objective           1.000000e+00
 norm of grad(f)                      1.243620e+01
 lagrangian violation                 2.689883e-15
 feasibility violation                0.000000e+00
 dual feasibility violation          -1.061311e-15
 optimizer runtime sec's              4.000000e-02


 optimal value of f =  -3.11520313228557e+00

 optimal solution  x =
  6.44088590010323e-01  1.16443609098553e+00

  multipliers are relativ to scf=1
  nr.    constraint      normgrad (or 1)   multiplier
    1   5.6621374e-15    1.3306996e+00    9.3456094e+00
    2   4.1078252e-15    2.5344912e+00   -1.0613110e-15
    3   6.4408859e-01    1.0000000e+00    0.0000000e+00
    4   1.1644361e+00    1.0000000e+00    0.0000000e+00

 evaluations of restrictions and their gradients
 (    30,     8) (    30,    10) (     0,     0) (     0,     0)
last estimate of condition of active gradients  1.000e+00
last estimate of condition of approx. hessian   1.000e+00
iterative steps total               9
# of restarts                       2
# of full regular updates           4
# of updates                        7
# of full regularized SQP-steps     0