spoptimset

Create/alter a sparse grid optimization OPTIONS structure.

Syntax

spoptimset
OPTIONS = spoptimset('NAME1',VALUE1,'NAME2',VALUE2,...)
OPTIONS = spoptimset(OLDOPTS,'NAME1',VALUE1,...)
OPTIONS = spoptimset(OLDOPTS,NEWOPTS)

Description

spoptimset with no input arguments displays all property names and their possible values.

OPTIONS = spoptimset('NAME1',VALUE1,'NAME2',VALUE2,...) creates an options structure OPTIONS in which the named properties have the specified values. Any unspecified properties have default values. It is sufficient to type only the leading characters that uniquely identify the property. Case is ignored for property names.

OPTIONS = spoptimset(OLDOPTS,'NAME1',VALUE1,...) alters an existing options structure OLDOPTS.

OPTIONS = spoptimset(OLDOPTS,NEWOPTS) combines an existing options structure OLDOPTS with a new options structure NEWOPTS. Any new properties overwrite corresponding old properties.

Properties

Property	Value {default}	Description
Minimize	{on} | off	If set to on, the optimization algorithm will search for a minimizer.
Maximize	on | {off}	If set to on, the optimization algorithm will search for a maximizer (searching for the minimizer and the maximizer at the same time is allowed). Note that searching for a maximizer is currently not supported by spcgsearch.
TolX	positive scalar {1e-4}	Termination tolerance on X. Note that the tolerance on X is taken with respect to the problem being re-scaled to the unit interval in each coordinate direction. That is, for instance, a sparse grid interpolant defined for the box [0,1e6]x[0,1e-6] with TolX = 0.1 would mean a break tolerance of 1e5 in x1 and a tolerance of 1e-7 in x2-direction. This parameter does not apply to spcgsearch.
TolFun	positive scalar {1e-6}	The search is terminated when the change of the function value from one iteration to the next is smaller than TolFun.
MaxIter	integer {100}	Maximum number of allowed iterations.
StartPoint	{best} | random | Dx1 vector	Start search from best available, random, or specified start point.
TestCorners	on | {off}	Specifically includes the 2^D corner points of the search box as potential start points of the search.
PrevResult	(d+1)x{1|2} double array	Specifies a possible best start point, such as from a previous search over a subdomain of the current search box. Format: [xoptmin;ymin xoptmax;ymax], where xoptmin and xoptmax are column vectors. Depending on the contents of the Minimize and Maximize fields, minima and/or maxima information should be provided. PrevResult is only considered as a start point if StartPoint is set to best.
Method	{spcgsearch} | {spcompsearch} | spfminsearch	Specifies the method used by the multiple random start search spmultistart. spcgsearch is the default for the Chebyshev grid, otherwise, it is spcompsearch.
NumStarts	integer {10}	Number of local searches to perform for the multiple random start method spmultistart. The following points are considered: (best) + (NumStarts-1 random points).
OptimsetOptions	struct {[]}	This feature is useful if additional configuration of the fminsearch algorithm used by spfminsearch is required beyond the parameters available through spoptimset. Example: opions = spoptimset('Optimset', optimset('FunValCheck','on'));
Display	{off} | iter	Optionally, displays information at each iteration.

Examples

As a preliminary to the following example, we construct a sparse grid interpolant of a test function (Branin's function) as follows.

f = inline(['(5/pi*x-5.1/(4*pi^2)*x.^2+y-6).^2 +' ...
            '10*(1-1/(8*pi))*cos(x)+10']);
range = [-5 10; 0 15];
options = spset('keepFunctionValues','on', 'GridType', 'Chebyshev', ...
  'DimensionAdaptive', 'on', 'DimAdaptDegree', 1, 'MinPoints', 10, ...
        'RelTol', 1e-6);
z = spvals(f, 2, range, options);

A typical case of a modification of the sparse grid optimization options structure is given by the need to specify a more stringent error tolerance on the function value to be used by the spcgsearch algorithm.

optoptions = spoptimset('TolFun', 1e-10);
format long e;
[xopt, fval] = spcgsearch(z, [], optoptions)
format short e;

xopt =
     3.141592655097273e+00
     2.274999997132531e+00
fval =
     3.978873577297303e-01

See Also

spoptimget.