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3  TOMVIEW /NPSOL Solver Reference

The NPSOL solvers are a set of Fortran solvers that were developed by the Stanford Systems Optimization Laboratory (SOL). Table 1 lists the solvers included in TOMVIEW /NPSOL. The solvers are called using a solver VI developed as part of TOMVIEW. All functionality of the NPSOL solvers are available and changeable in the TOMVIEW framework in LabVIEW.

Detailed descriptions of the TOMVIEW /NPSOL solvers are given in the following sections.

The solvers reference guides for the TOMVIEW /NPSOL solvers are available for download from the TOMVIEW home page http://tomopt.com/tomview/. There is also detailed instruction for using the solvers in Section 4.

TOMVIEW /NPSOL solves nonlinear optimization problems (con) defined as
 
min
x
f(x)
   
s/t
xL ≤ x ≤ xU,
bL ≤ A x ≤ bU
cL ≤ c(x) ≤ cU
    (1)
where x, xL, xU ∈ Rn, f(x) ∈ R, A ∈ Rm1 × n, bL,bU ∈ Rm1 and cL,c(x),cU ∈ Rm2.

quadratic programming (qp) problems defined as
 
min
x
f(x) =
1
2
xT F x + cT x
   
s/t
xL ≤ x ≤ xU,
bL ≤ A x ≤ bU
    (2)
where c, x, xL, xU ∈ Rn, F ∈ Rn × n, A ∈ Rm1 × n, and bL,bU ∈ Rm1.

linear programming (lp) problems defined as
 
min
x
f(x) = cT x
   
s/t
xL ≤ x ≤ xU,
bL ≤ A x ≤ bU
    (3)
where c, x, xL, xU ∈ Rn, A ∈ Rm1 × n, and bL,bU ∈ Rm1.

linear least squares (lls) problems defined as
 
min
x
f(x) =
1
2
|| C x − d ||
   
s/t
xL ≤ x ≤ xU,
bL ≤ A x ≤ bU
    (4)
where x, xL, xU ∈ Rn, d ∈ RM, C ∈ RM × n, A ∈ Rm1 × n, bL,bU ∈ Rm1.

and constrained nonlinear least squares problems defined as
 
min
x
f(x) =
1
2
r(x)T r(x)
   
s/t
xL ≤ x ≤ xU,
bL ≤ A x ≤ bU
cL ≤ c(x) ≤ cU
    (5)
where x, xL, xU ∈ Rn, r(x) ∈ RM, A ∈ Rm1 × n, bL,bU ∈ Rm1 and cL,c(x),cU ∈ Rm2.



Table 1: The SOL optimization solvers in TOMVIEW /NPSOL.
Function Description Reference  
MINOS 5.5 Sparse linear and nonlinear programming with linear and nonlinear constraints. [13]  
QPOPT 1.0-10 Non-convex quadratic programming with dense constraint matrix and sparse or dense quadratic matrix. [8]  
LSSOL 1.05-4 Dense linear and quadratic programs (convex), and constrained linear least squares problems. [7]  
NLSSOL 5.0-2 Constrained nonlinear least squares. NLSSOL is based on NPSOL. No reference except for general NPSOL reference. [9]  
NPSOL 5.02 Dense linear and nonlinear programming with linear and nonlinear constraints. [9]  

3.1  MINOS

3.1.1  Reference

Purpose
minos solves nonlinear optimization problems defined as

 
min
x
f(x)
   
s/t
xL ≤ x ≤ xU,
bL ≤ A x ≤ bU
cL ≤ c(x) ≤ cU
    (6)


where x, xL, xU ∈ Rn, f(x) ∈ R, A ∈ Rm1 × n, bL,bU ∈ Rm1 and cL,c(x),cU ∈ Rm2.


Calling Syntax
Using the driver routine tomRun:

assign_*.vi
tomRun.vi



Description of Inputs
Prob, The following fields are used:
 
x_L, x_U Bounds on variables.
 
b_L, b_U Bounds on linear constraints.
 
c_L, c_U Bounds on nonlinear constraints.
 
A Linear constraint matrix.
 
QP.c Linear coefficients in objective function.
 
 
 

Description of Outputs
Result, The following fields are used:
 
 
Result The structure with results.
f_k Function value at optimum.
x_k Solution vector.
x_0 Initial solution vector.
g_k Gradient of the function.
c_k Nonlinear constraint residuals.
 
cJac Nonlinear constraint gradients.
 
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;
cState State of nonlinear constraints. Free == 0; Lower == 1; Upper == 2; Equality == 3;
 
v_k Lagrangian multipliers (for bounds + dual solution vector).
 
ExitFlag Exit status from minos.
 
Inform Result of MINOS run.
 
  0 Optimal solution found.
  1 The problem is infeasible.
  2 The problem is unbounded (or badly scaled).
  3 Too many iterations.
  4 Apparent stall. The solution has not changed for a large number of iterations (e.g. 1000).
  5 The Superbasics limit is too small.
  6 User requested termination (by returning bad value).
  7 Gradient seems to be giving incorrect derivatives.
  8 Jacobian seems to be giving incorrect derivatives.
  9 The current point cannot be improved.
  10 Numerical error in trying to satisfy the linear constraints (or the linearized nonlinear constraints). The basis is very ill-conditioned.
  11 Cannot find a superbasic to replace a basic variable.
  12 Basis factorization requested twice in a row. Should probably be treated as inform = 9.
  13 Near-optimal solution found. Should probably be treated as inform = 9.
 
  20 Not enough storage for the basis factorization.
  21 Error in basis package.
  22 The basis is singular after several attempts to factorize it (and add slacks where necessary).
  30 An OLD BASIS file had dimensions that did not match the current problem.
  32 System error. Wrong number of basic variables.
  40 Fatal errors in the MPS file.
  41 Not enough storage to read the MPS file.
  42 Not enough storage to solve the problem.
 
rc Vector of reduced costs, g − ( A I )Tπ, where g is the gradient of the objective function if xn is feasible, or the gradient of the Phase-1 objective otherwise. If ninf = 0, the last m entries are −π. Reduced costs vector is of n+m length.
 
Iter Number of iterations.
FuncEv Number of function evaluations.
GradEv Number of gradient evaluations.
ConstrEv Number of constraint evaluations.
 
QP.B Basis vector in TOMVIEW QP standard.
 
MinorIter Number of minor iterations.
 
Solver Name of the solver (minos).
SolverAlgorithm Description of the solver.
 

3.1.2  Options

Description
Use missing value (-999 or less), when no change of parameter setting is wanted. The default value will then be used by MINOS, unless the value is altered in the SPECS file.
Definition: nnL = max(nnObj,nnJac))

Description of Blocks and Parameters

The following fields are used:
SPECS keyword text Lower Default Upper Comment
 
 
Printing
 
PRINT FILE File name for printing
SUMM FILE File name for summary file
SPECS FILE File to read options from
 
 
Print Levels
 
PRINT LEVEL 0 0 11111 JFLXB: Jac, fCon, lambda, x, B=LU stats
PRINT FREQUENCY 0 100  
SUMMARY FREQUENCY 0 100  
SOLUTION 0 1 1 1 = YES; 0 = NO
 
 
SLC Method 1
 
ROW TOLERANCE >0 1E-6
OPTIMALITY TOLERANCE >0 max(1E−6,(10epsR)0.5) = 1.73E-6
FEASIBILITY TOLERANCE >0 1E-6
LINESEARCH TOLERANCE >0 0.1 <1
MAXIMIZE 0 0 1 1=maximize
LAGRANGIAN 0 1 1 1=YES, 0=NO
PENALTY PARAMETER 0.0 1.0
MAJOR ITERATIONS LIMIT >0 50
MINOR ITERATIONS LIMIT >0 40
DERIVATIVE LEVEL 0 3 3 0,1,2,3
Is always set by minos dependent on Prob.ConsDiff, Prob.NumDiff.
 
RADIUS OF CONVERGENCE 0.0 0.01
FUNCTION PRECISION >0 3.0E-13   eps0.8=epsR
 
 
SLC Method 2
 
DIFFERENCE INTERVAL >0 5.48E-7   eps0.4
CENTRAL DIFFERENCE INTERVAL >0 6.69E-5   eps0.8/3
COMPLETION 0 1 LC,0 NC 1 0=PARTIAL 1=FULL
UNBOUNDED STEP SIZE >0 1E10
UNBOUNDED OBJECTIVE >0 1E20
SUPERBASICS LIMIT 1 50 1+nnL
TOMVIEW default (to avoid termination with Superbasics Limit too small):
If n <= 5000: max(50,n+1)
If n > 5000: max(500,n+200−size(A,1)−length(cL))
Avoid setting REDUCED HESSIAN (number of columns in reduced Hessian).
It will then be set to the same value as the SUPERBASICS LIMIT by MINOS.
 
HESSIAN DIMENSION 1 50 1+nnL
 
 
LP Subproblem
 
PIVOT TOLERANCE >0 3.25E-11   eps0.67
CRASH OPTION 0 3 3 0,1,2,3
WEIGHT ON LINEAR OBJECTIVE 0.0 0.0   during Phase 1
ITERATIONS LIMIT 0 3(m+m3) + 10nnL
m3=1 if length(Prob.QP.c) > 0, otherwise m3=0.
TOMVIEW default: max(10000,3(m+m3) + 10nnL).
 
PARTIAL PRICE 1 10 or 1   10 for LP
 
 
LU Options
 
LU FACTORIZATION TOLERANCE 1 100 or 5   100 if LP
LU UPDATE TOLERANCE 1 10 or 5   10 if LP
LU SWAP TOLERANCE >0 1.22E-4   eps1/4
LU SINGULARITY TOLERANCE >0 3.25E-11   eps0.67
LU PARTIAL PIVOTING 0 0 3 0=partial
or LU COMPLETE PIVOTING       1=complete
or LU ROOK PIVOTING       2=rook
 
 
Other options
 
CHECK FREQUENCY >0 60
EXPAND FREQUENCY >0 10000
FACTORIZATION FREQUENCY >0 50
AIJ TOLERANCE 0 1E-10
Elements |a(i,j)| < AIJ TOLERANCE are set as 0
 
SUBSPACE >0 0.5 1 Subspace tolerance
Convergence tolerance in current subspace before consider moving off
another constraint.
 
VERIFY LEVEL -1 -1 3 -1,0,1,2,3
 
 

3.2  QPOPT

3.2.1  Reference

Purpose
qpopt solves quadratic optimization problems defined as

 
min
x
f(x) =
1
2
xT F x + cT x
   
s/t
xL ≤ x ≤ xU,
bL ≤ A x ≤ bU
    (7)
where c, x, xL, xU ∈ Rn, F ∈ Rn × n, A ∈ Rm1 × n, and bL,bU ∈ Rm1.


Calling Syntax
Using the driver routine tomRun:

assign_qp.vi
tomRun.vi



Description of Inputs
Prob, The following fields are used:
 
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.
 
 
 

Description of Outputs
Result, The following fields are used:
 
 
Result The 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.
 
Inform Result of QPOPT run. 0 = Optimal solution found.
 
  0: x is a unique local minimizer. This means that x is feasible (it satisfies the constraints to the accuracy requested by the Feasibility tolerance), the reduced gradient is negligible, the Lagrange multipliers are optimal, and the reduced Hessian is positive definite. If H is positive definite or positive semidefinite, x is a global minimizer. (All other feasible points give a higher objective value.) Otherwise, the solution is a local minimizer, which may or may not be global. (All other points in the immediate neighborhood give a higher objective.)
 
  1: A dead-point was reached. This might occur if H is not sufficiently positive definite. If H is positive semidefinite, the solution is a weak minimizer. (The objective value is a global optimum, but there may be infinitely many neighboring points with the same objective value.) If H is indefinite, a feasible direction of decrease may or may not exist (so the point may not be a local or weak minimizer).
 
  At a dead-point, the necessary conditions for optimality are satisfied (x is feasible, the reduced gradient is negligible, the Lagrange multipliers are optimal, and the reduced Hessian is positive semidefinite.) However, the reduced Hessian is nearly singular, and/or there are some very small multipliers. If H is indefinite, x is not necessarily a local solution of the problem. Verification of optimality requires further information, and is in general an NP-hard problem [22].
 
  2: The solution appears to be unbounded. The objective is not bounded below in the feasible region, if the elements of x are allowed to be arbitrarily large. This occurs if a step larger than Infinite Step would have to be taken in order to continue the algorithm, or the next step would result in a component of x having magnitude larger than Infinite Bound. It should not occur if H is sufficiently positive definite.
 
  3: The constraints could not be satisfied. The problem has no feasible solution.
 
  4: One of the iteration limits was reached before normal termination occurred. See Feasibility Phase Iterations and Optimality Phase Iterations.
 
  5: The Maximum degrees of freedom is too small. The reduced Hessian must expand if further progress is to be made.
 
  6: An input parameter was invalid.
 
  7: The Problem type was not recognized.
 
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 TOMVIEW QP standard.
 
MinorIter Number of minor iterations. Not Set.
 
Solver Name of the solver (QPOPT).
SolverAlgorithm Description of the solver.
 

3.2.2  Options

Description
Use missing value (-999 or less), when no change of parameter setting is wanted. The default value will then be used by QPOPT, unless the value is altered in the SPECS file.


Description of Blocks and Parameters

The following fields are used:
SPECS keyword text Lower Default Upper Comment
 
 
Printing
 
PRINT FILE File name for printing
SUMM FILE File name for summary file
SPECS FILE File to read options from
 
 
Print Levels
 
PRINT LEVEL 0 10   0,1,5,10,20,30
 
 
Convergence Tolerances
 
OPTIMALITY TOLERANCE >0 1.1E-8   sqrt(eps)
FEASIBILITY TOLERANCE >0 1.1E-8   sqrt(eps)
 
 
Other options
 
CRASH TOLERANCE 0 0.01 <1
RANK TOLERANCE >0 1.1E-14   100*eps
ITERATION LIMIT >0 max(50,5(n+m))
MIN SUM YES (or NO) 0 0 1 1=min infeas.
IF 1 (MIN SUM YES), minimize the infeasibilities before return.
 
FEASIBILITY PHASE ITERATIONS >0 max(50,5(n+m))
INFINITE STEP SIZE >0 1E20
HESSIAN ROWS 0 n n 0 if FP or LP
Implicitly given by the dimensions of H in the call from LabVIEW
 
MAX DEGREES OF FREEDOM 0 n n
ONLY USED IF HESSIAN ROWS == N
CHECK FREQUENCY >0 50
EXPAND FREQUENCY >0 5
 
 

3.3  LSSOL

3.3.1  Reference

Purpose
lssol solves least squares optimization problems defined as

 
min
x
f(x) =
1
2
|| C x − d ||
   
s/t
xL ≤ x ≤ xU,
bL ≤ A x ≤ bU
    (8)
where x, xL, xU ∈ Rn, d ∈ RM, C ∈ RM × n, A ∈ Rm1 × n, bL,bU ∈ Rm1.


Calling Syntax
Using the driver routine tomRun:

assign_lls.vi
tomRun.vi



Description of Inputs
Prob, The following fields are used:
 
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.
 
 
 

Description of Outputs
Result, The following fields are used:
 
 
Result The 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 lssol.
Inform LSSOL information parameter.
  0 = Optimal solution with unique minimizer found.
  1 = Weak local solution (nonunique) was reached.
  2 = The solution appears to be unbounded.
  3 = The constraints could not be satisfied. The problem has no feasible solution.
  4 = Too many iterations, in either phase.
  5 = 50 changes of working set without change in x, cycling?
  6 = An input parameter was invalid.
  Other = UNKNOWN LSSOL Inform value.
 
 
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 TOMVIEW QP standard.
 
MinorIter Number of minor iterations. NOT SET.
 
Solver Name of the solver (LSSOL).
SolverAlgorithm Description of the solver.
 

3.3.2  Options

Description
Use missing value (-999 or less), when no change of parameter setting is wanted. The default value will then be used by LSSOL, unless the value is altered in the SPECS file.


Description of Blocks and Parameters

The following fields are used:
SPECS keyword text Lower Default Upper Comment
 
 
Printing
 
PRINT FILE File name for printing
SUMM FILE File name for summary file
SPECS FILE File to read options from
 
 
Print Levels
 
PRINT LEVEL 0 10   0,1,5,10,20,30
 
 
Convergence Tolerances
 
OPTIMALITY TOLERANCE >0 1.1E-8   sqrt(eps)
FEASIBILITY TOLERANCE >0 1.1E-8   sqrt(eps)
 
 
Other options
 
CRASH TOLERANCE >0 0.01 <1
RANK TOLERANCE >0 1.1E-14   100*eps
ITERATIONS LIMIT >0 max(50,5(n+m))
FEASIBILITY PHASE ITERATIONS >0 max(50,5(n+m))
INFINITE STEP SIZE >0 1E20
INFINITE BOUND SIZE >0 1E20
 
 

3.4  NLSSOL

3.4.1  Reference

Purpose
nlssol solves constrained nonlinear least squares problems defined as

 
min
x
f(x) =
1
2
r(x)T r(x)
   
s/t
xL ≤ x ≤ xU,
bL ≤ A x ≤ bU
cL ≤ c(x) ≤ cU
    (9)
where x, xL, xU ∈ Rn, r(x) ∈ RM, A ∈ Rm1 × n, bL,bU ∈ Rm1 and cL,c(x),cU ∈ Rm2.


Calling Syntax
Using the driver routine tomRun:

assign_cls.vi
tomRun.vi



Description of Inputs
Prob, The following fields are used:
 
x_L, x_U Bounds on variables.
 
b_L, b_U Bounds on linear constraints.
 
c_L, c_U Bounds on nonlinear constraints.
 
A Linear constraint matrix.
 
 
 

Description of Outputs
Result, The following fields are used:
 
 
Result The structure with results (see ResultDef.m).
f_k Function value at optimum.
x_k Solution vector.
x_0 Initial solution vector.
g_k Gradient of the function.
 
r_k Residual vector.
J_k Jacobian matrix.
c_k Nonlinear constraint residuals.
 
cJac Nonlinear constraint gradients.
 
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;
cState State of nonlinear constraints. Free == 0; Lower == 1; Upper == 2; Equality == 3;
 
v_k Lagrangian multipliers (for bounds + dual solution vector).
 
ExitFlag Exit status from nlssol.
Inform NLSSOL information parameter.
  0 = Optimal solution found.
  1 = Optimal solution found but not to requested accuracy.
  2 = No feasible point for the linear constraints.
  3 = No feasible point for the nonlinear constraints.
  4 = Too many major iterations.
  5 = Problem is unbounded, or badly scaled.
  6 = The current point cannot be improved on.
  7 = Large errors found in the derivatives.
  9 = An input parameter is invalid.
  Other = User requested termination
 
 
rc Reduced costs. If ninf=0, last m == -v_k.
 
Iter Number of iterations.
FuncEv Number of function evaluations.
GradEv Number of gradient evaluations.
ConstrEv Number of constraint evaluations.
 
QP.B Basis vector in TOMVIEW QP standard.
 
MinorIter Number of minor iterations.
 
Solver Name of the solver (nlssol).
SolverAlgorithm Description of the solver.
 

3.4.2  Options

Description
Use missing value (-999 or less), when no change of parameter setting is wanted. The default value will then be used by NLSSOL, if not the value is altered in the SPECS file (input SpecsFile)


Description of Blocks and Parameters

The following fields are used:
SPECS keyword text Lower Default Upper Comment
 
 
Printing
 
PRINT FILE File name for printing
SUMM FILE File name for summary file
SPECS FILE File to read options from
 
 
Print Levels
 
PRINT LEVEL 0 10   0,1,5,10,20,30
MINOR PRINT LEVEL 0 0   0,1,5,10,20,30
 
 
Convergence Tolerances
 
NONLINEAR FEASIBILITY TOLERANCE >0 1.1E-8   sqrt(eps)
OPTIMALITY TOLERANCE >0 3.0E-13   eps0.8
LINEAR FEASIBILITY TOLERANCE >0 1.1E-8   sqrt(eps)
 
 
Other options 1
 
CRASH TOLERANCE >0 0.01 <1
LINESEARCH TOLERANCE >0 0.9 <1
ITERATIONS LIMIT >0 max(50,3(n+m_L)+10*m_N)
MINOR ITERATIONS LIMIT >0 max(50,3(n+m_L+m_N))
STEP LIMIT >0 2
DERIVATIVE LEVEL 0 3 3 0,1,2,3
FUNCTION PRECISION >0 3.0E-13   eps0.8=epsR
DIFFERENCE INTERVAL >0 5.48E-8   eps0.4
CENTRAL DIFFERENCE INTERVAL >0 6.70E-5   eps0.8/3
INFINITE STEP SIZE >0 max(BIGBND,1E10)
INFINITE BOUND SIZE >0 1E10   = BIGBND
INITIAL HESSIAN (JTJ) 0 1   0 = UNIT
 
 
Other options 2
 
RESET FREQUENCY 0 2    
HESSIAN YES or NO 0 0   1 = YES
VERIFY LEVEL -1 -1 3 -1,0,1,2,3
 
 

3.5  NPSOL

3.5.1  Reference

Purpose
npsol solves dense nonlinear optimization problems defined as

 
min
x
f(x)
   
s/t
xL ≤ x ≤ xU,
bL ≤ A x ≤ bU
cL ≤ c(x) ≤ cU
    (10)


where x, xL, xU ∈ Rn, f(x) ∈ R, A ∈ Rm1 × n, bL,bU ∈ Rm1 and cL,c(x),cU ∈ Rm2.


Calling Syntax
Using the driver routine tomRun:

assign_*.vi
tomRun.vi



Description of Inputs
Prob, The following fields are used:
 
x_L, x_U Bounds on variables.
 
b_L, b_U Bounds on linear constraints.
 
c_L, c_U Bounds on nonlinear constraints.
 
A Linear constraint matrix.
 
 
 

Description of Outputs
Result, The following fields are used:
 
 
Result The structure with results (see ResultDef.m).
f_k Function value at optimum.
x_k Solution vector.
x_0 Initial solution vector.
g_k Gradient of the function.
c_k Nonlinear constraint residuals.
 
cJac Nonlinear constraint gradients.
 
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;
cState State of nonlinear constraints. Free == 0; Lower == 1; Upper == 2; Equality == 3;
 
v_k Lagrangian multipliers (for bounds + dual solution vector).
 
ExitFlag Exit status from npsol.
Inform NPSOL information parameter.
  0 = Optimal solution found.
  1 = Optimal solution found but not to requested accuracy.
  2 = No feasible point for the linear constraints.
  3 = No feasible point for the nonlinear constraints.
  4 = Too many major iterations.
  6 = The current point cannot be improved on.
  7 = Large errors found in the derivatives.
  9 = An input parameter is invalid.
  Other = User requested termination
 
rc Reduced costs. If ninf=0, last m == -v_k.
 
Iter Number of iterations.
FuncEv Number of function evaluations.
GradEv Number of gradient evaluations.
ConstrEv Number of constraint evaluations.
 
QP.B Basis vector in TOMVIEW QP standard.
 
MinorIter Number of minor iterations.
 
Solver Name of the solver (npsol).
SolverAlgorithm Description of the solver.
 

3.5.2  Options

Description
Use missing value (-999 or less), when no change of parameter setting is wanted. The default value will then be used by NPSOL, if not the value is altered in the SPECS file (input SpecsFile).


Description of Inputs

The following fields are used:
SPECS keyword text Lower Default Upper Comment
 
 
Printing
 
PRINT FILE File name for printing
SUMM FILE File name for summary file
SPECS FILE File to read options from
 
 
Print Levels
 
PRINT LEVEL 0 10   0,1,5,10,20,30
MINOR PRINT LEVEL 0 0   0,1,5,10,20,30
 
 
Convergence Tolerances
 
NONLINEAR FEASIBILITY TOLERANCE >0 1.1E-8   sqrt(eps)
OPTIMALITY TOLERANCE >0 3.0E-13   eps0.8
LINEAR FEASIBILITY TOLERANCE >0 1.1E-8   sqrt(eps)
 
 
Other options 1
 
CRASH TOLERANCE >0 0.01 <1
Note: Decision variables will be set to the closest bound to the starting point
based on this tolerance before running the optimization.
LINESEARCH TOLERANCE >0 0.9 <1
 
ITERATIONS LIMIT >0 max(50,3(n+m_L)+10*m_N)
MINOR ITERATIONS LIMIT >0 max(50,3(n+m_L+m_N))
STEP LIMIT >0 2
DERIVATIVE LEVEL 0 3 3 0,1,2,3
Is set by npsol dependent on Prob.ConsDiff, Prob.NumDiff
FUNCTION PRECISION >0 3.0E-13   eps0.8=epsR
DIFFERENCE INTERVAL >0 5.48E-8   eps0.4
CENTRAL DIFFERENCE INTERVAL >0 6.70E-5   eps0.8/3
INFINITE STEP SIZE >0 max(BIGBND,1E10)
INFINITE BOUND SIZE >0 1E10   = BIGBND
HESSIAN YES or NO 0 0   1 = YES
 
 
Other options 1
 
VERIFY LEVEL -1 -1 3 -1,0,1,2,3
 

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