a1.txt

非线性回归问题SQP解法

*******************************************************
*     INPUT DATE READ FROM"     ex8.2.txt   "         *
*******************************************************

NUMBER OF VARIASLES =  2
NUMBER OF EQUALITY CONSTRAINTS =  1
NUMBER OF INEQUALITY CONSTRAINTS =  1
INTIAL POINT:
       X(  1) =      .50000
       X(  2) =     1.00000

* ITERATION    0*
PENALTY FUNCTION =    -1.25000 (PENALTY PARAMETER =     1.000)
OBJECTIVE FUNCTION =    -1.50000
EQUALITY CONSTRAINTS:
     -.25000
INEQUALITY CONSTRAINTS:
      .75000
VARIABLES:
      .50000     1.00000
LAGRANGE MULTIPLIERS:
      .00000      .00000
ONE-DEMENSIONAL SEACH-BASIC SEARCH DIRECTION
NORM OF BASIC SEARCH DIRECTION=      .21250
STEP-SIZE=     1.00000

* ITERATION    1*
PENALTY FUNCTION =    -1.31500 (PENALTY PARAMETER =     1.000)
OBJECTIVE FUNCTION =    -1.55000
EQUALITY CONSTRAINTS:
     -.21250
INEQUALITY CONSTRAINTS:
     -.02250
VARIABLES:
      .85000      .70000
LAGRANGE MULTIPLIERS:
      .65000      .00000
SOLVE MODIFIED QP SUBPROBLEM TO OBTAIN SECOND-ORDER CORRECTION
ONE-DEMENSIONAL SEACH-SECOND ORDER SEARCH DIRECTION
NORM OF BASIC SEARCH DIRECTION=      .00907
STEP-SIZE=     1.00000

* ITERATION    2*
PENALTY FUNCTION =    -1.40813 (PENALTY PARAMETER =     1.000)
OBJECTIVE FUNCTION =    -1.41704
EQUALITY CONSTRAINTS:
     -.00892
INEQUALITY CONSTRAINTS:
      .08434
VARIABLES:
      .75806      .65899
LAGRANGE MULTIPLIERS:
      .64750      .00000
SOLVE MODIFIED QP SUBPROBLEM TO OBTAIN SECOND-ORDER CORRECTION
ONE-DEMENSIONAL SEACH-SECOND ORDER SEARCH DIRECTION
NORM OF BASIC SEARCH DIRECTION=      .00810
STEP-SIZE=     1.00000

* ITERATION    3*
PENALTY FUNCTION =    -1.41347 (PENALTY PARAMETER =     1.000)
OBJECTIVE FUNCTION =    -1.41509
EQUALITY CONSTRAINTS:
     -.00162
INEQUALITY CONSTRAINTS:
      .24009
VARIABLES:
      .69373      .72136
LAGRANGE MULTIPLIERS:
      .71184      .00000
SOLVE MODIFIED QP SUBPROBLEM TO OBTAIN SECOND-ORDER CORRECTION
ONE-DEMENSIONAL SEACH-SECOND ORDER SEARCH DIRECTION
NORM OF BASIC SEARCH DIRECTION=      .00205
STEP-SIZE=      .10000

* ITERATION    4*
PENALTY FUNCTION =    -1.41356 (PENALTY PARAMETER =     1.000)
OBJECTIVE FUNCTION =    -1.41524
EQUALITY CONSTRAINTS:
     -.00168
INEQUALITY CONSTRAINTS:
      .23241
VARIABLES:
      .69701      .71823
LAGRANGE MULTIPLIERS:
      .68866      .00000
SOLVE MODIFIED QP SUBPROBLEM TO OBTAIN SECOND-ORDER CORRECTION
ONE-DEMENSIONAL SEACH-SECOND ORDER SEARCH DIRECTION
NORM OF BASIC SEARCH DIRECTION=      .00111
STEP-SIZE=      .10000

* ITERATION    5*
PENALTY FUNCTION =    -1.41364 (PENALTY PARAMETER =     1.000)
OBJECTIVE FUNCTION =    -1.41526
EQUALITY CONSTRAINTS:
     -.00162
INEQUALITY CONSTRAINTS:
      .22676
VARIABLES:
      .69938      .71589
LAGRANGE MULTIPLIERS:
      .69469      .00000
SOLVE MODIFIED QP SUBPROBLEM TO OBTAIN SECOND-ORDER CORRECTION
ONE-DEMENSIONAL SEACH-SECOND ORDER SEARCH DIRECTION
NORM OF BASIC SEARCH DIRECTION=      .00102
STEP-SIZE=      .10000

* ITERATION    6*
PENALTY FUNCTION =    -1.41370 (PENALTY PARAMETER =     1.000)
OBJECTIVE FUNCTION =    -1.41528
EQUALITY CONSTRAINTS:
     -.00158
INEQUALITY CONSTRAINTS:
      .22133
VARIABLES:
      .70164      .71364
LAGRANGE MULTIPLIERS:
      .69321      .00000
SOLVE MODIFIED QP SUBPROBLEM TO OBTAIN SECOND-ORDER CORRECTION
ONE-DEMENSIONAL SEACH-SECOND ORDER SEARCH DIRECTION
NORM OF BASIC SEARCH DIRECTION=      .00082
STEP-SIZE=      .10000

* ITERATION    7*
PENALTY FUNCTION =    -1.41374 (PENALTY PARAMETER =     1.000)
OBJECTIVE FUNCTION =    -1.41528
EQUALITY CONSTRAINTS:
     -.00153
INEQUALITY CONSTRAINTS:
      .21645
VARIABLES:
      .70367      .71160
LAGRANGE MULTIPLIERS:
      .69327      .00000
SOLVE MODIFIED QP SUBPROBLEM TO OBTAIN SECOND-ORDER CORRECTION
ONE-DEMENSIONAL SEACH-SECOND ORDER SEARCH DIRECTION
NORM OF BASIC SEARCH DIRECTION=      .00066
STEP-SIZE=      .10000

* ITERATION    8*
PENALTY FUNCTION =    -1.41377 (PENALTY PARAMETER =     1.000)
OBJECTIVE FUNCTION =    -1.41525
EQUALITY CONSTRAINTS:
     -.00148
INEQUALITY CONSTRAINTS:
      .21206
VARIABLES:
      .70548      .70977
LAGRANGE MULTIPLIERS:
      .69332      .00000
SOLVE MODIFIED QP SUBPROBLEM TO OBTAIN SECOND-ORDER CORRECTION
ONE-DEMENSIONAL SEACH-SECOND ORDER SEARCH DIRECTION
NORM OF BASIC SEARCH DIRECTION=      .00054
STEP-SIZE=      .10000

* ITERATION    9*
PENALTY FUNCTION =    -1.41380 (PENALTY PARAMETER =     1.000)
OBJECTIVE FUNCTION =    -1.41522
EQUALITY CONSTRAINTS:
     -.00142
INEQUALITY CONSTRAINTS:
      .20812
VARIABLES:
      .70710      .70811
LAGRANGE MULTIPLIERS:
      .69336      .00000
SOLVE MODIFIED QP SUBPROBLEM TO OBTAIN SECOND-ORDER CORRECTION
ONE-DEMENSIONAL SEACH-SECOND ORDER SEARCH DIRECTION
NORM OF BASIC SEARCH DIRECTION=      .00043
STEP-SIZE=      .10000

* ITERATION   10*
PENALTY FUNCTION =    -1.41381 (PENALTY PARAMETER =     1.000)
OBJECTIVE FUNCTION =    -1.41518
EQUALITY CONSTRAINTS:
     -.00136
INEQUALITY CONSTRAINTS:
      .20457
VARIABLES:
      .70855      .70662
LAGRANGE MULTIPLIERS:
      .69340      .00000
SOLVE MODIFIED QP SUBPROBLEM TO OBTAIN SECOND-ORDER CORRECTION
ONE-DEMENSIONAL SEACH-SECOND ORDER SEARCH DIRECTION
NORM OF BASIC SEARCH DIRECTION=      .00000
STEP-SIZE=     1.00000

* ITERATION   11*
PENALTY FUNCTION =    -1.41421 (PENALTY PARAMETER =     1.000)
OBJECTIVE FUNCTION =    -1.41421
EQUALITY CONSTRAINTS:
      .00000
INEQUALITY CONSTRAINTS:
      .20807
VARIABLES:
      .70671      .70751
LAGRANGE MULTIPLIERS:
      .70697      .00000


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*              COMPUTATIONAL RESULTS              *
*******************************************************

OPTIMAL SOLUTION:

OBJECTIVE FUNCTION=    -1.41421
PENALTY FUNCTION =    -1.41421
(PENALTY PARAMETER =     1.00000)

VARIABLES:              (GRADIENT OF LAGRANGIAN:)
X(  1)=      .70671     (     -.00077)
X(  2)=      .70751     (      .00036)

EQUALKITY CONSTRAINTS:    LAGRANGE MULTIPLIERS:
C(  1)=      .00000       U(  1)=      .70697

INEQUALITY CONSTRAINTS:   LAGRANGE MULTIPLIERS:
C(  2)=      .20807       U(  2)=      .00000

MUNBER OF MAJOR ITERATIONS =   11

NUMBER OF QP PROBLEMS SOLVED =   21

MUNBER OF QP ITERATIONS =    0

MUNBER OF FUNCTION VALUES =   30

MUNBER OF GRADIENT VALUES =   23