SimPEG.optimization.ProjectedGradient.minimize

ProjectedGradient.minimize(evalFunction, x0)

Minimizes the function (evalFunction) starting at the location x0.

Parameters

• evalFunction (callable) – function handle that evaluates: f, g, H = F(x)

• x0 (numpy.ndarray) – starting location

Return type

numpy.ndarray

Returns

x, the last iterate of the optimization algorithm

evalFunction is a function handle:

(f[, g][, H]) = evalFunction(x, return_g=False, return_H=False )

def evalFunction(x, return_g=False, return_H=False):
    out = (f,)
    if return_g:
        out += (g,)
    if return_H:
        out += (H,)
    return out if len(out) > 1 else out[0]

The algorithm for general minimization is as follows:

startup(x0)
printInit()

while True:
    doStartIteration()
    f, g, H = evalFunction(xc)
    printIter()
    if stoppingCriteria(): break
    p = findSearchDirection()
    p = scaleSearchDirection(p)
    xt, passLS = modifySearchDirection(p)
    if not passLS:
        xt, caught = modifySearchDirectionBreak(p)
        if not caught: return xc
    doEndIteration(xt)

print_done()
finish()
return xc