TOMLAB Appendix B

This page is part of the TOMLAB Manual. See TOMLAB Manual.

Result - the Output Result Structure

The results of the optimization attempts are stored in a structure array named Result. The currently defined fields in the structure are shown in #Table: Information stored in the optimization result structure Result.. The use of structure arrays make advanced result presentation and statistics possible. Results from many runs may be collected in an array of structures, making postprocessing on all results easy.

When running global optimization, output results are also stored in mat-files, to enable fast restart (warm start) of the solver. It is seldom the case that one knows that the solver actually converged for a particular problem. Therefore one does restarts until the optimum does not change, and one is satisfied with the results. The information stored in the mat-file glbSave.mat by the solver glbSolve is shown in #Table: Information stored in the mat-file glbSave.mat by the solver glbSolve. Used for automatic restarts.. The information stored in the mat-file glcSave.mat by the solver glcSolve is shown in #Table: Information stored in the mat-file glcSave.mat by the solver glcSolve. Used for automatic restarts.:. Different information is stored when using glbFast and glcFast, see the solver reference.

Table: Information stored in the mat-file glbSave.mat by the solver glbSolve. Used for automatic restarts.

Variable	Description
C	Matrix with all rectangle centerpoints, in [0,1]-space.
D	Vector with distances from centerpoint to the vertices.
DMin	Row vector of minimum function value for each distance.
DSort	Row vector of all different distances, sorted.
E	Computed tolerance in rectangle selection.
F	Vector with function values.
L	Matrix with all rectangle side lengths in each dimension.
Name	Name of the problem. Used for security if doing warm start.
glbfMin	Best function value found at a feasible point.
iMin	The index in D which has lowest function value, i.e. the rectangle which minimizes (F - glbfMin + E)./D where E = max(EpsGlob * abs(glbfMin), 1E - 8).

Table: Information stored in the mat-file glcSave.mat by the solver glcSolve. Used for automatic restarts.

Variable	Description
C	Matrix with all rectangle centerpoints.
D	Vector with distances from centerpoint to the vertices.
F	Vector with function values.
G	Matrix with constraint values for each point.
Name	Name of the problem. Used for security if doing warm start.
Split	Split(i, j) is the number of splits along dimension i of rectangle j.
T	T (i) is the number of times rectangle i has been trisected.
fMinEQ	sum(abs(infeasibilities)) for minimum points, 0 if no equalities.
fMinIdx	Indices of the currently best points.
feasible	Flag indicating if a feasible point has been found.
glcf_min	Best function value found at a feasible point.
iL	iL(i, j) is the lower bound for rectangle j in integer dimension I(i).
iU	iU (i, j) is the upper bound for rectangle j in integer dimension I (i).
ignoreidx	Rectangles to be ignored in the rectangle selection procedure.
s	s(j) is the sum of observed rates of change for constraint j.
s_0	s_0 is used as s(0).
t	t(i) is the total number of splits along dimension i.

Table: Information stored in the optimization result structure Result.

Field	Description
Name	Problem name.
P	Problem number.
probType	TOMLAB problem type, according to Table in TOMLAB Overall Design.
Solver	Solver used.
SolverAlgorithm	Solver algorithm used.
solvType	TOMLAB solver type.
ExitFlag	0 if convergence to local min. Otherwise errors.
ExitText	Text string describing the result of the optimization. Inform Information parameter, type of convergence.
CPUtime	CPU time used in seconds.
REALtime	Real time elapsed in seconds.
Iter	Number of major iterations.
MinorIter	Number of minor iterations (for some solvers).
maxTri	Maximum rectangle size.
FuncEv	Number of function evaluations needed.
GradEv	Number of gradient evaluations needed.
HessEv	Number of Hessian evaluations needed.
ConstrEv	Number of constraint evaluations needed.
ConJacEv	Number of constraint Jacobian evaluations needed.
ConHessEv	Number of nonlinear constraint Hessian evaluations needed.
ResEv	Number of residual evaluations needed (least squares).
JacEv	Number of Jacobian evaluations needed (least squares).
x_k	Optimal point.
f_k	Function value at optimum.
g_k	Gradient value at optimum.
B_k	Quasi-Newton approximation of the Hessian at optimum.
H_k	Hessian value at optimum.
y_k	Dual parameters.
v_k	Lagrange multipliers for constraints on variables, linear and nonlinear constraints.
r_k	Residual vector at optimum.
J_k	Jacobian matrix at optimum.
Ax	Value of linear constraints at optimum.
c_k	Value of nonlinear constraints at optimum.
cJac	Constraint Jacobian at optimum.
x_0	Starting point.
f_0	Function value at start i.e. f (x 0).
c_0	Value of nonlinear constraints at start.
Ax0	Value of linear constraints at start.
xState	State of each variable, described in <.
bState	State of each linear constraint, described in Table 151.
cState	State of each general constraint, described in Table 152.
p_dx	Matrix where each column is a search direction.
alphaV	Matrix where row i stores the step lengths tried for the i:th iteration.
x_min	Lowest x-values in optimization. Used for plotting.
x_max	Highest x-values in optimization. Used for plotting.
LS	Structure with statistical information for least squares problems, see #Table: Information stored in the structure Result.LS..
F_X	F_X is a global matrix with rows: [iter no f(x)].
SepLS	General result variable with fields z and Jz. Used when running separable nonlinear least squares problems.
QP	Structure with special fields for QP problems. Used for warm starts, see TOMLAB Appendix A.
SOL	Structure with some of the fields in the Prob.SOL structure, the ones needed to do a warm start of a SOL solver, see TOMLAB Appendix A. The routine WarmDefSOL moves the relevant fields back to Prob.SOL for the subse- quent call.
DUNDEE	Structure with special result fields from TOMLAB /MINLP solvers.
plotData	Structure with plotting parameters.
Prob	Problem structure, see TOMLAB Appendix A. Please note that certain solvers that do reformulations of the problem, e.g. L1Solve, infSolve and slsSolve, return the Prob structure of the reformulated problem in this field, not the original one.

The field xState describes the state of each of the variables. In #Table: The state variable xState for the variable. the different values are described. The different conditions for linear constraints are defined by the state variable in field bState. In #Table: The state variable bState for each linear constraint. the different values are described.

Table: The state variable xState for the variable.

Value	Description
0	A free variable.
1	Variable on lower bound.
2	Variable on upper bound.
3	Variable is fixed, lower bound is equal to upper bound.

Table: The state variable bState for each linear constraint.

Value	Description
0	Inactive constraint.
1	Linear constraint on lower bound.
2	Linear constraint on upper bound.
3	Linear equality constraint.

Table: The state variable cState for each nonlinear constraint.

Value	Description
0	Inactive constraint.
1	Nonlinear constraint on lower bound.
2	Nonlinear constraint on upper bound.
3	Nonlinear equality constraint.

Table: Information stored in the structure Result.LS.

Field	Description
SSQ	rTk rk .
Covar	Covariance matrix (inverse of JTk · Jk ).
sigma2	Estimate of squared standard deviation.
Corr	Correlation matrix (normalized covariance matrix).
StdDev	Estimated standard deviation in parameters.
x	The optimal point x_k.
ConfLim	95% confidence limit (roughly) assuming normal distribution of errors.
CoeffVar	Coefficients of variation of estimates.