defaultEquMu: Default settings for equality handling mechanism
In SACOBRA: Self-Adjusting COBRA

Description Usage Details Value See Also

Sets suitable defaults for the equality handling part of SACOBRA.

The EH technique transforms each equality constraint h(\vec{x})=0 into two inequality constraints h(\vec{x})-μ <0 and -h(\vec{x})-μ<0 with an adaptively decaying margin μ.

If refine parameter is set to TRUE, then a refine mechanism is applied to shift the best found solution within the equality margin μ toward the feasible subspace by minimizing the sum of squared constraint surrogates with a conjugate gradient method.

\mbox{Minimize}\quad ∑_i( max(0,g_i(x))^2 ) + ∑_j ( h_j(x)^2 )

1	defaultEquMu()

With the call setOpts(equHandle,defaultEquMu()) it is possible to extend a partial list equHandle list which is set by user to a list containing all equHandle-elements (the missing ones are taken from defaultEquMu()). These settings are used by cobraInit for initializing the equality margin μ and by the internal functions updateCobraEqu and modifyMu. The minimization step of refine mechanism is done by L-BFGS-B method in optim function from stats package.

equHandle, a list with the following elements:

`active`	[TRUE] if set to TRUE the equality-handling (EH) technique is activated. The EH technique transforms each equality constraint h(\vec{x})=0 into two inequality constraints h(\vec{x})-μ <0 and -h(\vec{x})-μ<0 with an adaptively decaying margin μ.
`equEpsFinal`	[1e-07] lower bound for margin μ. `equEpsFinal` should be set to a small but non-zero value (larger than machine accuracy).
`initType`	["TAV"] the equality margin μ can be initialized with one of these approaches: ["TAV"\|"TMV"\|"EMV"\|"useGrange"] TAV: (Total Absolute Violation) takes the median of the sum of violations of the initial population. TMV: (Total Maximum Violation) takes the median of the maximum violation of the initial population EMV: takes the median of the maximum violation of equality constraints of the initial population useGrange: takes the average of the ranges of the equality constraint functions
`epsType`	["SAexpFunc"] type of the function used to modify margin μ during the optimization process can be one of ["SAexpFunc"\|"expFunc"\|"Zhang"\|"CONS"]. see `modifyMu`.
`dec`	[1.5] decay factor for margin μ. see `modifyMu`
`refine`	[TRUE] enables the refine mechanism f the equality handling mechanism.
`refineMaxit`	maximum number of iterations used in the refine step. Note that the refine step runs on the surrogate models and does not impose any extra real function evaluation.