OpenMx (version 2.17.3)

mxComputeGradientDescent: Optimize parameters using a gradient descent optimizer

Description

This optimizer does not require analytic derivatives of the fit function. The fully open-source CRAN version of OpenMx offers 2 choices, CSOLNP and SLSQP (from the NLOPT collection). The OpenMx Team's version of OpenMx offers the choice of three optimizers: CSOLNP, SLSQP, and NPSOL.

Usage

mxComputeGradientDescent(
  freeSet = NA_character_,
  ...,
  engine = NULL,
  fitfunction = "fitfunction",
  verbose = 0L,
  tolerance = NA_real_,
  useGradient = NULL,
  warmStart = NULL,
  nudgeZeroStarts = mxOption(NULL, "Nudge zero starts"),
  maxMajorIter = NULL,
  gradientAlgo = mxOption(NULL, "Gradient algorithm"),
  gradientIterations = imxAutoOptionValue("Gradient iterations"),
  gradientStepSize = imxAutoOptionValue("Gradient step size")
)

Arguments

freeSet

names of matrices containing free parameters.

...

Not used. Forces remaining arguments to be specified by name.

engine

specific 'CSOLNP', 'SLSQP', or 'NPSOL'

fitfunction

name of the fitfunction (defaults to 'fitfunction')

verbose

integer. Level of run-time diagnostic output. Set to zero to disable

tolerance

how close to the optimum is close enough (also known as the optimality tolerance)

useGradient

whether to use the analytic gradient (if available)

warmStart

a Cholesky factored Hessian to use as the NPSOL Hessian starting value (preconditioner)

nudgeZeroStarts

whether to nudge any zero starting values prior to optimization (default TRUE)

maxMajorIter

maximum number of major iterations

gradientAlgo

one of c('forward','central')

gradientIterations

number of Richardson iterations to use for the gradient

gradientStepSize

the step size for the gradient

Details

One option for CSOLNP and SLSQP is gradientAlgo. CSOLNP uses forward method by default, while SLSQP uses central method. forward method requires 1 time gradientIterations function evaluation per parameter per gradient, while central method requires 2 times gradientIterations function evaluations per parameter per gradient. Users can change the default methods for either of these optimizers. NPSOL usually uses the forward method, but adaptively switches to central under certain circumstances.

CSOLNP uses the value of argument gradientStepSize as-is, whereas SLSQP internally scales it by a factor of 100. The purpose of this transformation is to obtain roughly the same accuracy given other differences in numerical procedure. NPSOL ignores gradientStepSize, and instead uses a function of mxOption “Function precision” to determine its gradient step size.

All three optimizers can use analytic gradients, and only NPSOL uses warmStart.

References

Luenberger, D. G. & Ye, Y. (2008). Linear and nonlinear programming. Springer.

Examples

# NOT RUN {
data(demoOneFactor)
factorModel <- mxModel(name ="One Factor",
  mxMatrix(type="Full", nrow=5, ncol=1, free=FALSE, values=0.2, name="A"),
    mxMatrix(type="Symm", nrow=1, ncol=1, free=FALSE, values=1, name="L"),
    mxMatrix(type="Diag", nrow=5, ncol=5, free=TRUE, values=1, name="U"),
    mxAlgebra(expression=A %*% L %*% t(A) + U, name="R"),
  mxExpectationNormal(covariance="R", dimnames=names(demoOneFactor)),
  mxFitFunctionML(),
    mxData(observed=cov(demoOneFactor), type="cov", numObs=500),
     mxComputeSequence(steps=list(
     mxComputeGradientDescent(),
     mxComputeNumericDeriv(),
     mxComputeStandardError(),
     mxComputeHessianQuality()
    )))
factorModelFit <- mxRun(factorModel)
factorModelFit$output$conditionNumber # 29.5
# }