Common input for all CGO solvers

Input parameters

Prob structure

The following fields are used in the problem description structure Prob
Field	Description
Name	Name of the problem. Used for security when doing warm starts.
FUNCS.f	The routine to compute the function, given as a string, e.g. CGOF.
FUNCS.c	The routine to compute the nonlinear constraint, e.g. CGOC.
x_L	Lower bounds for each element in x. Must be finite.
x_U	Upper bounds for each element in x. Must be finite.
b_L	Lower bounds for the linear constraints.
b_U	Upper bounds for the linear constraints.
A	Linear constraint matrix.
c_L	Lower bounds for the nonlinear constraints.
c_U	Upper bounds for the nonlinear constraints.
WarmStart	If true, >0, the solver reads the output from the last run from the mat-file cgoSave.mat, and continues from the last run. If Prob.CGO.WarmStartInfo has been defined through a call to WarmDefGLOBAL, this field is used instead of the cgoSave.mat file. In the last case, exactly the same points are used. In the first case, a new test is made which points to use.
MaxCPU	Maximal CPU Time (in seconds) to be used.
user	User field used to send information to low-level functions.
PriLevOpt	Print Level. value output 0 Silent 1 Summary 2 Printing each iteration 3 Info about local / global solution 4 Progress in x.
PriLevSub	Print Level in subproblem solvers, see help in snSolve and gnSolve.
f_Low	Lower bound on the optimal function value. If defined, used to restrict the target values into interval ['f_Low,min(surface)].
optParam	Structure with optimization parameters. See the table below describing the fields used in the optParam structure.
CGO	Structure with parameters specific to costly global optimization. See the table below describing the fields used in the CGO structure.
MIP	Structure with parameters specific mixed integer optimization. See the table below describing the fields used in the MIP structure.

optParam structure

The most important field is MaxFunc, normally use default values for other fields.

fields used in Prob.optParam:
Field	Description
MaxFunc	Maximal number of costly function evaluations, default 300 for rbfSolve and arbfMIP, and default 200 for ego. MaxFunc must be <= 5000. If WarmStart = 1 and MaxFunc <= nFunc (Number of f(x) used) then set MaxFunc := MaxFunc + nFunc.
IterPrint	Print one information line each iteration, and the new x tried. Default IterPrint = 1. fMinI means the best f(x) is infeasible. fMinF means the best f(x) is feasible (also integer feasible).
fGoal	Goal for function value, not used if inf or empty.
eps_f	Relative accuracy for function value, fTol == eps_f. Stop if |f - f Goal| <= |fGoal| * fTol, if fGoal ≠ 0. Stop if |f - fGoal| <= fTol, if fGoal = 0. See the output field maxTri.
bTol	Linear constraint tolerance.
cTol	Nonlinear constraint tolerance.
MaxIter	Maximal number of iterations used in the local optimization on the re- sponse surface in each step. Default 1000, except for pure IP problems, then max(GO.MaxFunc, MaxIter);.

CGO structure

The CGO solvers need an initial set of at least n+1 points, where n = dim(x).
Either an initial Experimental Design is needed or the user may input its own choice of points, or a combination of both.
A warm start with points from previous run(s) using any CGO solver is also possible.

The input parameters for the Experimental Design are given as fields in Prob.CGO.
See help expDesign for details on how to set the following fields in Prob.CGO defining the Experimental Design:
Percent, nSample, X, F, Cc, RandState, AddMP, nTrial, CLHMethod
Note that the setting of RandState might influence parts of the CGO solvers as well.

fields used in Prob.CGO:
Field	Description
Percent	See expDesign for detailed information on how to set the experimental design parameters.
nSample
X
F
CX
RandState
AddMP
nTrial
CLHMethod
SCALE
objType	Tranformation of function F, all transformations are computed and saved. Selected objType is used in CGO interpolations. Value Transformation 0 No transformation (default). 1 Ft(1) = log10(F + Fadd), Fadd=10k, where k=1,2,...lowest k to assure F + Fadd > 0 2 Ft(2) = log(1+F) if F >= 0, -log(1-F) if F < 0 3 Ft(3) = log(F), if all(F) > 0, otherwise NaN 4 Ft(4) = -log(-F) transformation, if all(F) < 0, otherwise NaN 5 Ft(5) = -1/y transformation, if either all(F) < 0 or all(F) > 0, otherwise NaN 6 Ft(6) = F(F >= median(F)) = median(F) 7 Ft(7) = F(F > median(F)) = median(F) + log10(1+F+median(F)) 8 Ft(8) = F(F > 10REPLACE) = 104 + log10(1+F-10REPLACE)
REPLACE	In objType == 8, large function values Z are replaced by new values Replacement: Z:= FMAX + log10(Z-FMAX+1), where FMAX = 10REPLACE, Default REPLACE = 4.
XMIN	Matrix d x nLocal with nLocal minima previously found. Best point(s) found might be global minima Sampling of points will be avoided around these points, see epsDist below
FMIN	Column vector with nLocal costly function values f(x) computed at the nLocal points in XMIN
epsDist	If epsDist > 10-7, all points x in the sphere $\|x-XMIN(:,i)\|<=epsDist$ are excluded from the search. Default is epsDist = 0, then the solver does not try to detect local minima, and just continues until maxFunc reached
SMOOTH	= 1 The problem is smooth enough for local search using numerical gradient estimation methods = 0 the problem is nonsmooth or noisy, and local search methods using numerical gradient estimation are likely to produce garbage search directions.
globalSolver	Global optimization solver used for subproblem optimization. Default glcCluster (SMOOTH=1) or glcDirect (SMOOTH=0). If the global- Solver is [glcCluster|glcCluster]], the fields Prob.GO.maxFunc1, Prob.GO.maxFunc2, Prob.GO.maxFunc3, Prob.GO.localSolver, Prob.GO.DIRECT and other fields set in Prob.GO are used. See the help for these parameters in glcCluster.
localSolver	Local optimization solver used for subproblem optimization. If not defined, the TOMLAB default constrained NLP solver is used.