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9  Solution Output Files

The output file contains three sections.
  • The first section “geometric programming model” describes some problem characteristics, such as the number of variables, etc.

  • The second section “path-following solver for reformulated model” contains the running information during the iterative process. The primal and dual objective values represent the reformulated primal and dual problems.

  • The third section “solutions for original GP” contains the optimal values of the variables, the constraint functions, the primal and dual objective functions, and the feasibility residues of the original GP problem pair.

    The termination code 0–7 represents the following: 
      0=optimal: find an optimal solution;
  1=unbounded: the reformulated problem is unbounded;
  2=infeasible: the reformulated problem is infeasible;
  3=iteration limit: reach the iteration limit before desired accuracy;
  4=numerical difficulties: encounter numerical problems
  5=primal or dual infeasible: the original problems are infeasible;
  6=insufficient space: memory space is not sufficient;
  7=data file error: find input data errors.
    The last paragraph lists the CPU time: read in data, solve the problem and the sum of the two.
The following is the output file for Dembo68. 

                             =================
                             COPL_GP 1.1  2005
                             =================
               geometric programming optimizer


  geometric programming model
  ---------------------------
  primal gp vars . 2
  primal gp consts 1
  primal gp terms  4
  degree of diffic 1

  path-following solver for reformulated model
  --------------------------------------------

*- iter =   0        dual   value         =-2.00000000000000E+00
                     primal value         =-4.64038529823796E-17
    mu  = 9.233E-01  Dual   infeasibility = 3.608E-01
                     Primal infeasibility = 5.000E-01

*- iter =   1        dual   value         =-9.99533217451737E-01
                     primal value         =-3.62989378647483E-01
    mu  = 1.591E-01  Dual   infeasibility = 0.000E+00
                     Primal infeasibility = 1.872E-17

*- iter =   2        dual   value         =-7.13113168002422E-01
                     primal value         =-5.88706966976516E-01
    mu  = 3.544E-02  Dual   infeasibility = 2.294E-02
                     Primal infeasibility = 8.301E-17

*- iter =   3        dual   value         =-6.93636390346386E-01
                     primal value         =-6.89738422619333E-01
    mu  = 1.854E-03  Dual   infeasibility = 4.382E-03
                     Primal infeasibility = 2.975E-17

*- iter =   4        dual   value         =-6.93130105030368E-01
                     primal value         =-6.93115339650404E-01
    mu  = 9.392E-06  Dual   infeasibility = 2.847E-05
                     Primal infeasibility = 2.383E-17

*- iter =   5        dual   value         =-6.93147171812859E-01
                     primal value         =-6.93147164639831E-01
    mu  = 4.710E-09  Dual   infeasibility = 1.456E-08
                     Primal infeasibility = 4.592E-17

*- iter =   6        dual   value         =-6.93147180555572E-01
                     primal value         =-6.93147180551985E-01
    mu  = 2.355E-12  Dual   infeasibility = 7.282E-12
                     Primal infeasibility = 8.860E-17

*- iter =   7        dual   value         =-6.93147180559943E-01
                     primal value         =-6.93147180559941E-01
    mu  = 1.210E-15  Dual   infeasibility = 3.705E-15
                     Primal infeasibility = 5.133E-17

 -- exit : optimal solution obtained. iter 7

          dual objective value =-6.93147180559943E-01
          primal               =-6.93147180559941E-01
          Dual infeasibility   = 3.705E-15
          Primal               = 5.133E-17

  solutions for original GP
  -------------------------

 primal GP solution

        i               t(i)
        1  .421974819510E+01
        2  .236980965158E+00

 primal GP constraint value

        i   constraint value
        1  .750531607446E+00

 primal GP obj value (from direct comp)      2.00000000000000E+00
 primal GP infeasibility                     0.000E+00

 dual   GP obj value (from direct comp)      1.99999999999999E+00
 dual   GP infeasibility                     5.133E-17

  all done, termination code=    0
  0=optimal, 1=unbounded, 2=infeasible
  3=iteration limit, 4=numerical difficulties
  5=primal or dual infeasible, 6=insufficient space
  7=data file error

 ----- time for readin =        .02
               solving =        .01
 total time in seconds =        .03
Tolerances for primal and dual feasibilities and complementarity are specified as
  єP = 10−8,    єD = 10−8,    and єC = 10−12.         (19)
Extensive computational tests indicate that the requirement of єC = 10−12 is very strong. The solution stopping by this specification usually is very accurate.

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