Recurrent network expression and its property of replicator dynamics for optimization

Kazuaki Masuda, Eitaro Aiyoshi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

Replicator dynamics (RD) is a well-known mathematical model of evolutionary dynamics. In the study of optimization, a gradient dynamics called the variable metric gradient projection (VMGP) model, which is used to solve a constrained optimization problem with normalized equality and nonnegative inequalities, is known to have the structure of RD. In this paper, we show that the VMGP dynamics can also be considered to have the structure of recurrent neural network (N.N.) by introducing a new variable so as to transform the VMGP dynamics equivalently. We found that it is described as a new model similar to the well known Hopfield's N.N. by regarding the newly introduced variable as "inner state" and giving a particular nonlinear element as output unit of the network. We also provide some interesting properties of the network model through fixed point analysis for the nonlinear dynamics. Numerical simulations show the validity of our discussions.

Original languageEnglish
Title of host publicationConference Proceedings - IEEE International Conference on Systems, Man and Cybernetics
Pages3488-3493
Number of pages6
Volume4
DOIs
Publication statusPublished - 2004
Event2004 IEEE International Conference on Systems, Man and Cybernetics, SMC 2004 - The Hague, Netherlands
Duration: 2004 Oct 102004 Oct 13

Other

Other2004 IEEE International Conference on Systems, Man and Cybernetics, SMC 2004
CountryNetherlands
CityThe Hague
Period04/10/1004/10/13

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Keywords

  • Constrained optimization
  • Fixed point analysis
  • Nonlinear dynamical system
  • Recurrent network
  • Replicator dynamics

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Masuda, K., & Aiyoshi, E. (2004). Recurrent network expression and its property of replicator dynamics for optimization. In Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics (Vol. 4, pp. 3488-3493) https://doi.org/10.1109/ICSMC.2004.1400882