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 | r^{T}_{k} r_{k} . |
Covar | Covariance matrix (inverse of J^{T}_{k} · J_{k} ). |
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. |