Optimization

Handle optimization solver properties.

Syntax

model.sol(sname).create(fname,"Optimization")

model.sol(sname).feature(fname).set(pname,value)

model.sol(sname).feature(fname).create(aname,SolverAttribute)

Description

Operation feature. Use this feature to solve PDE-constrained optimization problems. The computed solution object contains the PDE solution evaluated for the optimal set of design variables. When the gradient-evaluation method is analytic, it also returns the adjoint solution.

The Optimization Module includes SNOPT and several other optimization solvers. See the Optimization Module Manual for details.

To add a stationary solver, substitute SolverAttribute above with StationaryAttrib. For a time-dependent solver, replace SolverAttribute with TimeAttrib.

Choosing solver is done with the following property

Table 6-51: Property/Value Pair to select optimization solver

Property	Value	Default	Description
optsolver	bobyqa | cobyla | coordsearch | lm | mma | montecarlo | neldermead | snopt	snopt	Optimization solver

The following table includes general optimization solver properties, which a common to all optimization solvers:

Table 6-52: General Optimization Properties

Property	Value	Default	Description
control	String	user	Name of the controlling study step or "user" if the feature is controlled manually.
keeplog	on | off	off	Keep warnings in stored log.
nsolvemax	positive integer	1000	Maximum number of objective evaluations.
opttol	real scalar	0.001	Tolerance.
plot	on | off	off	Whether to plot while solving.
plotgroup	String	default	Name of plot group for plot while solving.
probes	vector of strings		Probes to use if probesel=manual.
probesel	all | none | manual	all	The probes to compute.

When the optimization solver is set to SNOPT (snopt), the following properties are accepted:

Table 6-53: Valid Properties for optsolver snopt

Property	Value	Default	Description
clist	String array		Provide values for constants as input parameters using a string array; for the corresponding constant names, use cname.
cname	String array		Provide names of constants as input parameters using a string array; for the corresponding constant values, use clist.
feastol	real scalar	1e-6	Linear constraint tolerance.
funcprec	real scalar	3.8e-11	Function precision.
gradientmma	analytic | forward | adjoint | forward_numeric	analytic	Gradient/Jacobian evaluation method for MMA.
gradientsnopt	analytic | numeric	analytic	Gradient/Jacobian evaluation method for SNOPT.
hessupd	integer	10	Hessian updates.
linesearch	derivative | nonderivative	derivative	Use a derivative (gradient) or nonderivative (gradient free) linesearch strategy.
linestol	real scalar	0.9	Linesearch tolerance (a value between 0 and 1). A lower value gives a more accurate search.
majfeastol	real scalar	1e-6	Nonlinear constraint tolerance.
manualhessupd	on | off	off	Whether to use property hessupd.
manualstepcond	on | off	off	Whether to use manual step condition.
message	String		The log message from the last solution process.
objcontrib	all | manual	all	Whether to use all objective contributions present or specify manually.
optobj	String		Objective function that is minimized when objcontrib=manual.
pdistrib	on | off	off	Distribute parametric sweep.
qpsolver	cholesky | cg | qn	cholesky	QP subproblem algorithm.
stepcond	String	empty	Manual step condition.

The property gradientsnopt is used to control if the gradient should be computed analytically (by solving the adjoint problem) or numerically. If the number of design variables is large, numerical computation of the gradient can be very time consuming. Analytic gradient is only supported when the underlying PDE-problem is stationary.

If manualstepcond is set to on, the expression in the property stepcond is evaluated when new values for the design variables have been computed. If the expression becomes negative, the new values are discarded and the optimization solver reduces the step length in the current line search.

When the optimization solver is set to Levenberg-Marquardt (lm), the following properties are accepted:

Table 6-54: Valid Properties for optsolver lm

Property	Value	Default	Description
gradientlm	numeric	numeric	Gradient/Jacobian evaluation method.
gradorder	first | second	first	Approximation order of the gradient.
lmfact	real scalar	1e-3	Initial Levenberg-Marquardt factor.

When the optimization solver is set to MMA, the following properties are accepted:

Table 6-55: Valid Properties for optsolver MMA

Property	Value	Default	Description
mmamaxiter	positive integer	1	Maximum outer iterations.
mmamaxiteractive	on | off	off	Enable maximum outer iterations.
mmainnmax	positive integer	10	Maximum inner iterations per outer iteration.
mmagepsfactor	real scalar	0.1	Internal tolerance factor.
mmacfactor	real scalar	1000	Constraint penalty factor.
mmaghinit	real scalar	0.5	Initial asymptote factor (ghinit).
mmaghdecr	real scalar	0.7	Decreasing asymptote factor (ghdecr).
mmaghincr	real scalar	1.2	Increasing asymptote factor (ghincr).
mmaasymin	real scalar	0.01	Minimum asymptote level (asymin).
mmaasymax	real scalar	10	Maximum asymptote level (asymax).
mmaalbeta	real scalar	0.1	Bounds asymptote factor (albefa).
mmaxxmove	real scalar	0.5	Bounds control factor (xxmove).
mmaraai	real scalar	0.00001	Approximation increment (raai).
mmaraamin	real scalar	0.000001	Lower approximation bound (raamin).
mmalsq	on | off	on	Automatically transform least-squares objectives to constraints for efficiency.
mmaminmax	on | off	on	Automatically transform minimax and maximin problems to constraints for efficiency.
gcmma	on | off	on	Use the globally convergent MMA algorithm.

For a description of the optimization properties, see Advanced Solver Properties in the Optimization Module User’s Guide.

Table 6-56: Removed femoptim Properties

Property	Reason
Callblevel	Handled by attribute features
Solprop	Handled by stationary or time
Solcomp	Handled by variables
Report	Handled by variables
Out	Solution should be exported