Solving linear programming problem with Nelder-Mead method

For solving linear programming problem, the simplex method is often applied to search for solution. On the other hand, the Nelder-Mead method is mostly applied as a non-linear searching technique. It would be interesting to see how well it is applied to a linear programming problem previously solved using the Simple Method in TI-84.

The Nelder-Mead method is ran under the TI Nspire CX CAS with NM program written in the TI Basic program. The program accepts arguments including the name of the function to maximize as a string and a list of initial parameters to execute the Nelder-Mead algorithm. The function itself is declared using piece-wise function to bound the return value to the function to maximize while giving penalty to values that violate any constraints (as in the inequalities of the standard simplex method).

Previous program in the TI-84 using the simplex method obtained {200,400} as the solution. The Nelder-Mead returned a solution very close to it.

nmsimplex

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2 thoughts on “Solving linear programming problem with Nelder-Mead method

  1. gmgolem Post author

    Thanks for the kind words! I am afraid that the TI basic program of the Nelder Mead method here need some clean-up before they are worth publishing.. In the meantime, for reference from an authoritative implementation, say in R, source code (in C) could be found from its github site https://github.com/wch/r-source by searching for optim.c

    Reply

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