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Nelder-Mead Simplex Optimization Routine for Large-Scale Problems: A Distributed Memory Implementation

  • Kyle Klein
  • Julian Neira

    ()

The Nelder-Mead simplex method is an optimization routine that works well with irregular objective functions. For a function of $$n$$ parameters, it compares the objective function at the $$n+1$$ vertices of a simplex and updates the worst vertex through simplex search steps. However, a standard serial implementation can be prohibitively expensive for optimizations over a large number of parameters. We describe an implementation of the Nelder-Mead method in parallel using a distributed memory. For $$p$$ processors, each processor is assigned $$(n+1)/p$$ vertices at each iteration. Each processor then updates its worst local vertices, communicates the results, and a new simplex is formed with the vertices from all processors. We also describe how the algorithm can be implemented with only two MPI commands. In simulations, our implementation exhibits large speedups and is scalable to large problem sizes. Copyright Springer Science+Business Media New York 2014

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File URL: http://hdl.handle.net/10.1007/s10614-013-9377-8
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Article provided by Society for Computational Economics in its journal Computational Economics.

Volume (Year): 43 (2014)
Issue (Month): 4 (April)
Pages: 447-461

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Handle: RePEc:kap:compec:v:43:y:2014:i:4:p:447-461
Contact details of provider: Web page: http://www.springerlink.com/link.asp?id=100248

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  1. Mark Huggett, 2003. "Human Capital and Earnings Distribution Dynamics," Working Papers gueconwpa~03-03-10, Georgetown University, Department of Economics.
  2. Aldrich, Eric M. & Fernández-Villaverde, Jesús & Ronald Gallant, A. & Rubio-Ramírez, Juan F., 2011. "Tapping the supercomputer under your desk: Solving dynamic equilibrium models with graphics processors," Journal of Economic Dynamics and Control, Elsevier, vol. 35(3), pages 386-393, March.
  3. Michael Creel, 2005. "User-Friendly Parallel Computations with Econometric Examples," Computational Economics, Society for Computational Economics, vol. 26(2), pages 107-128, October.
  4. Beaumont, Paul M & Bradshaw, Patrick T, 1995. "A Distributed Parallel Genetic Algorithm for Solving Optimal Growth Models," Computational Economics, Society for Computational Economics, vol. 8(3), pages 159-79, August.
  5. Swann, Christopher A, 2002. "Maximum Likelihood Estimation Using Parallel Computing: An Introduction to MPI," Computational Economics, Society for Computational Economics, vol. 19(2), pages 145-78, April.
  6. Donghoon Lee & Matthew Wiswall, 2007. "A Parallel Implementation of the Simplex Function Minimization Routine," Computational Economics, Society for Computational Economics, vol. 30(2), pages 171-187, September.
  7. Christopher Ferrall, 2005. "Solving Finite Mixture Models: Efficient Computation in Economics Under Serial and Parallel Execution," Computational Economics, Society for Computational Economics, vol. 25(4), pages 343-379, June.
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