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A  Prob - the Input Reference

The Input Problem Structure, here referred to as Prob, is one of the most central aspects of working with TOMVIEW. It contains numerous fields and substructures that created the problem instance.

Default values are automatically set for everything by the system.


Table 11: Information stored in the problem structure Prob. Fields defining sub-structures are defined in Table 12.
Field Description
 
TOMVIEW TOMVIEW Version number.
 
A Matrix with linear constraints, one constraint per row (dense or sparse).
 
b_L Lower bounds on the linear constraints.
b_U Upper bounds on the linear constraints.
c_L Lower bounds on the general constraints.
c_U Upper bounds on the general constraints.
 
CHECK If true, no more check is done by probCheck. Set to true (=1) after first call to probCheck.
 
CheckNaN If Prob.CheckNaN  =0, nlp_d2c, nlp_H, nlp_d2r checks for NaN elements and estimates the corresponding derivatives numerically. If Prob.CheckNaN >0, the same applies for nlp_dc, nlp_g, nlp_J. Off-diagonal elements in symmetric Hessians should both be set as NaN. fdng, fdng2, fdng3, only estimate NaN elements in gradient, if gradient vector is input.
 
cols The columns in the user computed matrix that will be accessed, and needs to be set.
 
ConIx A vector with the sequence of calls required to compute the numerical constraint Jacobian efficiently. See findpatt for more information.
 
ConsDiff Numerical approximation of the constraint derivatives. If set to 1, the classical approach with forward or backward differences together with automatic step selection will be used. If set to 2, 3 or 4 the spline routines csapi, csaps or spaps in the SPLINE Toolbox will be used. If set to 5, derivatives will be estimated by use of complex variables. For the SOL solvers, the value 6 gives the internal derivative approximation.
 
ConsPattern Matrix with non-zero pattern in the constraint gradient matrix.
 
d2cPattern Sparsity pattern of the d2c matrix.
 
d2LPattern Sparsity pattern of the Hessian of the Lagrangian function.
 
f_Low Lower bound on optimal function value.
f_opt Objective function value f(x*) corresponding to the points given in x_opt.
 
GradTolg Size of step length to estimate first order derivatives in the gradient vector.
GradTolH Size of step length to estimate the Hessian matrix.
GradTolJ Size of step length to estimate the Jacobian matrix or the constraint gradient matrix.
 
HessIx A vector with the sequence of calls required to compute the numerical Jacobian efficiently.
HessPattern Matrix with non-zero pattern in the Hessian matrix.
 
JacPattern Matrix with non-zero pattern in the Jacobian matrix.
 
LargeScale Flag if the problem is large scale. If this flag is set no collection of search steps are made. Also, for some solvers, LargeScale chooses between dense (=0) or sparse (=1) versions of the solver. This flag also controls several other features in TOMVIEW such as estimation of patterns.
 
MaxCPU Maximum execution time in seconds for the solver. The feature is available for a limited number of solvers.
 
N Problem dimension (number of variables).
 
mLin Number of linear constraints.
 
mNonlin Number of nonlinear constraints.
 
Name Problem name.
 
NumDiff Numerical approximation of the derivatives of the objective function. If set to 1, the classical approach with forward or backward differences together with automatic step selection will be used.
 
P Problem number (1).
 
PriLev Print level in the driver routines (0).
PriLevOpt Print level in the TOM solver.
 
probType TOMVIEW problem type, see Table 1.
 
rows The rows in the user computed vector/matrix that will be accessed, and needs to be set.
 
simType A flag indicating when the TOMVIEW simulation format is used. The objective and constraints are calculated at the same function. The gradient and Jacobian are also calculated in the same function.
 
smallA If 1 then small elements in the linear constraints are removed. The elements have to be smaller than eps*max(max(abs(Prob.A))).
 
SolverMIP Name of the Solver that should solve LP sub-problems.
SolverLP Name of the Solver that should solve LP sub-problems.
SolverQP Name of the solver that should solve QP sub problems.
 
WarmStart For solver with support for warmstarts, WarmStart > 0 indicates that the solver should do a warm start.
 
Warning Show warning messages.
 
x_0 Starting point.
 
x_L Lower bounds on the variables x.
x_U Upper bounds on the variables x.
 
x_opt Stationary points x*, one per row (if known). It is possible to define an extra column, in which a zero (0) indicates a minimum point, a one (1) a saddle point, and a two (2) a maximum. As default, minimum points are assumed. The corresponding function values for each row in x_opt should be given in Prob.f_opt.
 


Table 12: The fields defining sub-structures in the problem structure Prob. Default values are in all tables given in parenthesis at the end of each item.


Field Description
QP Structure with special fields for linear and quadratic problems, see Table 13.
LS Structure with special fields for least squares problems, see Table 14.
MIP Structure with special fields for mixed-integer programming, see Table 15.
FUNCS Structure with user defined names of the VI's computing the objective, gradient, Hessian etc. See Table 16. These routines are called from the corresponding gateway routine
Callbacks Structure with user defined names of the VI's computing the objective, gradient, Hessian etc. For special callback use.


Table 13: Information stored in the structure Prob.QP. The three last sub-fields, always part of the Prob subfields, could optionally be put here to give information to a subproblem QP, LP, dual LP or feasible point (Phase 1) solver.


Field Description
F Constant matrix F in 1/2 x'Fx+c'x
c Cost vector c in 1/2 x'Fx+c'x
D Matrix for linear minimax problems


Table 14: Information stored in the structure Prob.LS
Field Description
weightType Weighting type:
0 No weighting.
1 Weight with data in y. If y(t)=0, the weighting is 0, i.e. deleting this residual element.
2 Weight with weight vector or matrix in weightY. If weightY is a vector then weighting by weigthY.*r (element wise multiplication). If weightY is a matrix then weighting by weigthY*r (matrix multiplication).
3 nlp_r calls the routine weightY (must be a string with the routine name) to compute the residuals.
weightY Either empty, a vector, a matrix or a string, see weightType.
t Time vector t.
y Vector or matrix with observations y(t).
C Linear least squares matrix.
yUse If yUse =0 compute residual as f(x,t)−y(t) (default), otherwise y(t) should be treated separately by the solver and the residual routines just return f(x,t).
SepAlg If SepAlg=1, use separable non linear least squares formulation (default 0).


Table 15: Information stored in the structure Prob.MIP
Field Description
IntVars Which variables are integer valued
VarWeight Priority vector for each variable.
fIP Function value for point defined in xIP. Gives an upper bound on the IP value wanted. Makes it possible to cut branches and avoid node computations
xIP The point x giving the function value fIP.
SOS Special orders sets.


Table 16: Information stored in the structure Prob.FUNCS
Field Description
f Name of VI computing the objective function f(x).
g Name of VI computing the gradient vector g(x). If Prob.FUNCS.g is empty then numerical derivatives will be used.
H Name of VI computing the Hessian matrix H(x).
c Name of VI computing the vector of constraint functions c(x).
dc Name of VI computing the matrix of constraint normals ∂ c(x)/dx.
d2c Name of VI computing the 2nd part of 2nd derivative matrix of the Lagrangian function, Σi λi ∂2c(x)/dx2.
r Name of VI computing the residual vector r(x).
J Name of VI computing the Jacobian matrix J(x).
d2r Name of VI computing the 2nd part of the Hessian for nonlinear least squares problem, i.e. Σi=1m ri(x) ∂2ri(x) / ∂ xj ∂ xk.

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