evalReal: Evaluate new iterate on real function(s)
In SACOBRA: Self-Adjusting COBRA

Description Usage Arguments Details Value See Also

Helper for cobraPhaseII: The new iterate xNew, which was found by optimization on the surrogate models, is evaluated on the real function cobra$fn. In the case of equality constraints, evalReal does the additional refine step (see Details).

evalReal(
  cobra,
  ev1,
  xNew,
  fValue,
  feval,
  optimConv,
  optimTime,
  currentEps,
  fitnessSurrogate = cobra$fitnessSurrogate
)

`cobra`	an object of class COBRA, this is a (long) list containing all settings from `cobraPhaseII`
`ev1`	a list, initially empty, gradually filled by calls to `evalReal`
`xNew`	the new point, see `cobraPhaseII`
`fValue`	fitness value estimated for `xNew`
`feval`	function evaluations on surrogates needed by COBRA optimizer
`optimConv`	see `cobraPhaseII`
`optimTime`	see `cobraPhaseII`
`currentEps`	artificial current margin for the equality constraints: A point is said to be artificially feasible, if h_j(x) - currentEps ≤ 0, -h_j(x) - currentEps ≤ 0, for all equality constraints and if it is feasible in the inequality constraints.
`fitnessSurrogate`	[`cobra$fitnessSurrogate`] see `cobraPhaseII`

If cobra$equHandle$active==TRUE, then xNew is first refined: The artificially feasible solution xNew is replaced by a refined solution ev1$xNew. ev1$xNew is created by using optim to minimize the function

∑_i{\max(0,g_i(x))} + ∑_j{h_j^2(x) }

Ideally, the refined solution ev1$xNew should be on the equality constraints (within machine accuracy), but there is no guarantee that optim reaches this desired result.

ev1, a list with the following n-dim vectors ( n = number of iterations, the last element is from the new iterate / point xNew ):

`predY`	prediction of `fitnessSurrogate` at `xNew`
`predVal`	`fvalue` (fitness + penalty in case of NMKB et al.)
`feval`	function evaluations on surrogates needed by COBRA optimizer
`optimizerConvergence`	see `cobraPhaseII`
`optimizationTime`	see `cobraPhaseII`
`predC`	prediction of `cobra$constraintSurrogates` at `xNew`
`feas`	TRUE, if `xNew` is feasible for the current constraints
`feasPred`	TRUE, if `xNew` is feasible for `cobra$constraintSurrogates`

In addition, ev1 has these elements:

`xNew`	`d`-dim vector, the new point, refined in the case of equality handling
`xNewEval`	`cobra$fn(xNew)`, an `(1+nConstraints)`-dim vector (objective,constraints)
`newNumViol`	scalar, the number of constraint violations (above `cobra$conTol`) on true constraints from `xNewEval`
`newNumPred`	scalar, the number of constraint violations (above `cobra$conTol`) on constraint surrogates for `xNew`
`newMaxViol`	scalar, the maximum constraint violation (with `currentEps` subtracted) on true constraints from `xNewEval`
`trueMaxViol`	scalar, the maximum constraint violation (w/o `currentEps` subtracted) on true constraints from `xNewEval`

If cobra$equHandle$active==TRUE, then the last four values are for xNew after the refine step. In this case, the first three elements newNumViol, newNumPred, and newMaxViol refer to the artificially enlarged equality constraints, i.e.

h_j(x) - currentEps ≤ 0, -h_j(x) - currentEps ≤ 0,

and the true inequality constraints max(0,g_i(x)). The last element trueMaxViol measures the maximum violation among the true equality constraints |h_j(x)| and the true inequality constraints max(0,g_i(x)).

cobraPhaseII

SACOBRA documentation built on March 26, 2020, 7:15 p.m.