TOMLAB OPTIMIZATION ENVIRONMENT: qpoptTL

qpoptTL

Purpose

TOMLAB QPOPT QP/LP Interface

Syntax

   Result = qpoptTL(Prob);

Description

For a problem description, see qpAssign.

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 not used) from previous run (Warm start).
 iState    State for the constraints from previous run (Warm start).
 cLamda    Lagrangian multipliers from previous run (Warm start).
 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. Fields not defined in optParam is defined by a call to SOLSet.m

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

 #   SPECS keyword text            Lower    Default   Upper   Comment
 Printing
 1.  PRINT LEVEL                   0        10                {0,1,5,10,20,30}
 3.  PRINT FILE                    0        0                 Fortran Unit #
           SET BY INTERFACE IF PrintFile is given
 4.  SUMMARY FILE                  0        0                 Fortran Unit #
           SET BY INTERFACE IF SummFile  is given
 10. OPTIMALITY TOLERANCE          >0       1.1E-8            sqrt(eps)
     -optParam.eps_x; 
 11. FEASIBILITY TOLERANCE         >0       1.1E-8            sqrt(eps)
     -optParam.bTol; 
 21. CRASH TOLERANCE               >0       0.01      <1      
 27. RANK TOLERANCE                >0       1.1E-14           100*eps
     -optParam.eps_Rank;
 30. ITERATION LIMIT               >0       max(50,5(n+m))    
     -optParam.MaxIter;
 33. MIN SUM YES (or NO)           0        0         1       1=min infeas
           IF 1 (MIN SUM YES), minimize the infeasibilities before return
 36. FEASIBILITY PHASE ITERATIONS  >0       max(50,5(n+m))    
     -optPar(36)=optParam.MinorIter;
 45. INFINITE STEP SIZE            >0       1E20
 47. HESSIAN ROWS                  0        n         n       0 if FP or LP
           IMPLICITLY GIVEN BY THE DIMENSIONS OF H IN THE CALL FROM MATLAB
 48. MAX DEGREES OF FREEDOM        0        n         n       
           ONLY USED IF HESSIAN ROWS == N
 51. CHECK FREQUENCY               >0       50
 52. EXPAND FREQUENCY              >0       5

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 qpopt.m (similar to TOMLAB).
 Inform   QPOPT 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 (QPOPT).
 SolverAlgorithm  Description of the solver.

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

 xs       Solution and slack variables.
 cLamda   Lagrangian multipliers.
 iState   State for variables and constraints in iState.

See Also

qpopt