The MAXQUAD Test Function

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Description

Lemarechal's MAXQUAD optimization test function.

Usage

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maxquad(n, m)

Arguments

n

number of variables of the generated test function.

m

number of functions to compete for the maximum.

Details

MAXQUAD actually is a family of minimax functions, parametrized by the number n of variables and the number m of functions whose maximum it is.

Value

Returns a list with components fn the generated test function of n variables, and gr the corresponding (analytical) gradient function.

References

Kuntsevich, A., and F. Kappel (1997). SolvOpt – The Solver for Local Nonlinear Optimization Problems. Manual Version 1.1, Institute of Mathematics, University of Graz.

Lemarechal, C., and R. Mifflin, Eds. (1978). Nonsmooth Optimization. Pergamon Press, Oxford.

Shor, N. Z. (1985). Minimization Methods for Non-differentiable Functions. Series in Computational Mathematics, Springer-Verlag, Berlin.

Examples

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# Test function of 5 variables, defined as maximum of 5 smooth functions
maxq <- maxquad(5, 5)
fnMaxquad <- maxq$fn
grMaxquad <- maxq$gr
# shor