This is a conjugate gradient method. For a description see Mukai,H., Readily Implementable Conjugate Gradient Methods, Mathematical Programming, 17 (1979), 298-319.


NQ = i2 = 6*NP + 4


IER = Greater than 0 if optimum is achieved
IER = 3 Function value is accurate to relative ACC
IER = 2 Norm of gradient is less than ACC
IER = 1 Attempted stepsize is less than ACC (relatively)
IER = -1 Iteration limit exceeded
IER = -2 Function error on first call of FP
IER = -3 Input error
IER = -4 Not enough scratch storage
IER = -5 Continual straying into forbidden area
IER = -9 Function error in first FUNC call
IER =-16 Small gradient without meeting termination criteria
IER =-24 Gradient inaccurate---does not point uphill


Besides the general options, the following are available.


IV8 = 1 Use formula (14) in paper (Dixon method)
IV8 = 2 Use formula (15) in paper (Fletcher and Reeves) (Default = 2)
IV8 = 3 Use formula (22) in paper (Polak,Ribiere,Polyak)
IV8 = 4 Use formula (23) in paper (Mukai)
IV3 = 0 Use Step 3a in paper (Default = 0)
IV3 = 1 Use Step 3b in paper


ALPHA = Type of Lipschitz constant for stepsize (Default=0.1)
BETA = Used in searching for suitable step-length (Default=0.6) OMEGA = Used to insure that we have an ascent direction (Default=0.3)
EPSTIL = Upper bound for epsilon in Step 1 of algorithm (Default=1.D-3)
RH = Default step-length in Step 3. Function dependent. (Default=0.3)
DELTIL = First guess at smallest eigenvalue of quadratic approximation
(Default= 1.D-3)
SIGMA = Shrinkage factor for deltahat in Step 3b. (Default=0.5)
BIGL = Affects direction choice (Step 10). Function dependent.
AKAPPA = Relates to estimate of deltahat (Step 2). (Default=30.)

Note: Compared to other algorithms, MUKAI employs a large number of parameters. Experimentation with alternative values is likely to be profitable. The algorithm tends to do relatively well far from the optimum and relatively less well close to it if the function has narrow valleys or ridges.To refine the location of the optimum, the user may wish to use GRADX or some other algorithm after MUKAI terminates.

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