minosQPTL

Purpose

TOMLAB MINOS QP Interface

Syntax

   Result = minosqpTL(Prob);

Description

For a problem description, see qpAssign.

MINOS creates a print file (print.dat) and a summary file (summary.dat).

Input Parameters

 Prob   Problem structure in TOMLAB format

Fields used in input structure Prob (call Prob=qpAssign(...) or Prob=ProbDef; to define Prob)

 x_L, x_U  Bounds on variables. 
 b_L, b_U  Bounds on linear constraints. 
 A         Linear constraint matrix.
 QP.c      Linear coefficients in objective function.
 QP.F      Quadratic matrix of size nnObj x nnObj. nnObj < n is OK.
 PriLevOpt Print Level.
 WarmStart If true, use warm start, otherwise cold start.

Fields used in Prob.SOL:

 xs        Solution and slacks from previous run.
 hs        State for solution and slacks from previous run.
 nS        Number of superbasics from previous run.
 SpecsFile Name of user defined SPECS file, read BEFORE optPar() is used.
 PrintFile Name of SOL Print file. Amount and type of printing determined 
           by SPECS parameters or optPar parameters.
 SummFile  Name of SOL Summary File.
 optPar    Elements > -999 takes precedence over corresponding TOMLAB
           params.

Description of the optPar vector

optPar is a structure with optimization parameters.

MINOS keywords in optPar(#) - and the fields used in optParam

 #   SPECS keyword text            Lower    Default   Upper   Comment

 Printing
 1.  PRINT LEVEL                   0        0         1    0=brief 1=LU stats
 3.  PRINT FILE                    0        0         99      Fortran Unit #
 4.  SUMMARY FILE                  0        0         99      Fortran Unit #
 5.  PRINT FREQUENCY               0        100
 6.  SUMMARY FREQUENCY             0        1
 7.  SOLUTION YES/NO               0        1         1       1 = YES; 0 = NO
 8.  SUPPRESS PARAMETERS           0        0         1       1 = True

 Convergence Tolerances
 10. OPTIMALITY TOLERANCE          >0       max(1E-6,(10eps_R)^0.5) = 1.73E-6
     -optParam.eps_x
 11. FEASIBILITY TOLERANCE         >0       1E-6  
     -optParam.bTol

 Derivative checking
 13. VERIFY LEVEL                  -1       0         3       {-1,0,1,2,3}
 14. START OBJECTIVE CHECK AT COL  0        1         nnObj         
 15. STOP OBJECTIVE CHECK AT COL   0        nnObj     nnObj

 Scaling
 18. SCALE OPTION                  0        1         2
 19. SCALE TOLERANCE               >0       0.9       <1
 20. SCALE PRINT                   0        0         1       1 = True

 Other Tolerances
 21. CRASH TOLERANCE               0        0.1       <1
 22. LINESEARCH TOLERANCE          >0       0.9       <1
     -optParam.LineSearch.sigma

 Rank tolerance
 23. LU FACTOR TOLERANCE           1        5.0
 24. LU UPDATE TOLERANCE           1        5.0
 25  LU DENSITY TOLERANCE          >0       0.5                            
 26. LU SINGULARITY TOLERANCE      >0       3.25E-11          eps^(0.67)
 27. PIVOT TOLERANCE               >0       3.25E-11          eps^(0.67)
     -optParam.eps_Rank

 LP parameters
 28. CRASH OPTION                  0        3         3       {0,1,2,3}
 29. WEIGHT ON LINEAR OBJECTIVE    0.0      0.0               during Phase 1 
 30. ITERATION LIMIT               0        3m + 10nnObj
     -optParam.MaxIter
 31. PARTIAL PRICE                 1        1
 32. MAXIMIZE                      0        0         1       1=maximize

 Reduced-gradient method
 39. DERIVATIVE LEVEL              0        3         3       {0,1,2,3}
 41. FUNCTION PRECISION            >0       3.0E-13           eps^0.8=eps_R
     -optParam.fTol
 42. DIFFERENCE INTERVAL           >0       5.48E-8           eps^0.4
 43. CENTRAL DIFFERENCE INTERVAL   >0       6.70E-5           eps^{0.8/3}
 44. COMPLETION                    0      1 LC, 0 NC  1     0=PARTIAL 1=FULL
 45. UNBOUNDED STEP SIZE           >0       1E20
 46. UNBOUNDED OBJECTIVE           >0       1E10

 Hessian approximation
 47. HESSIAN DIMENSION             1        50        1+nnObj   
 48. SUPERBASICS LIMIT             1        50        1+nnObj

 Frequencies
 51. CHECK FREQUENCY               >0       60
 52. EXPAND FREQUENCY              >0       10000
 53. FACTORIZATION FREQUENCY       >0       50
 54. SAVE FREQUENCY                >0       100

 BASIS files
 55. OLD BASIS file                0        0
 56. NEW BASIS file                0        0
 57. BACKUP BASIS file             0        0
 58. INSERT file                   0        0
 59. PUNCH file                    0        0
 60. LOAD file                     0        0
 61. DUMP file                     0        0
 62. SOLUTION file                 0        0

 63. LU COMPLETE PIVOTING          0        0         1    1=complete,0=partial
     or LU PARTIAL PIVOTING                      

Output Parameters

 Result   Structure with results (see ResultDef.m):
 f_k      Function value at optimum.
 x_k      Solution vector.
 x_0      Initial solution vector.
 g_k      Exact gradient computed at optimum.
 xState   State of variables. Free == 0; On lower == 1; On upper == 2; 
          Fixed == 3;
 bState   State of linear constraints. Free == 0; Lower == 1; Upper == 2; 
          Equality == 3;
 v_k      Lagrangian multipliers (for bounds + dual solution vector).
 ExitFlag Exit status from minos.m (similar to TOMLAB).
 Inform   MINOS information parameter.
 rc       Reduced costs. If ninf=0, last m == -v_k.
 Iter     Number of iterations.
 FuncEv   Number of function evaluations. Set to Iter.
 GradEv   Number of gradient evaluations. Set to Iter.
 ConstrEv Number of constraint evaluations. Set to 0.
 QP.B     Basis vector in TOMLAB QP standard.
 MinorIter Number of minor iterations. NOT SET.
 Solver   Name of the solver (minos).
 SolverAlgorithm  Description of the solver.

The following output are set in the Result.SOL sub field

 xs       Solution and slack variables.
 hs       State for variables and slacks in xs.
 nS       # of superbasics.
 nInf     # of infeasibilities.
 sInf     Sum of infeasibilities.

See Also