TY - GEN
T1 - Recurrent network expression and its property of replicator dynamics for optimization
AU - Masuda, Kazuaki
AU - Aiyoshi, Eitaro
PY - 2004/12/1
Y1 - 2004/12/1
N2 - 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.
AB - 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.
KW - Constrained optimization
KW - Fixed point analysis
KW - Nonlinear dynamical system
KW - Recurrent network
KW - Replicator dynamics
UR - http://www.scopus.com/inward/record.url?scp=15744381425&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=15744381425&partnerID=8YFLogxK
U2 - 10.1109/ICSMC.2004.1400882
DO - 10.1109/ICSMC.2004.1400882
M3 - Conference contribution
AN - SCOPUS:15744381425
SN - 0780385667
T3 - Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics
SP - 3488
EP - 3493
BT - 2004 IEEE International Conference on Systems, Man and Cybernetics, SMC 2004
T2 - 2004 IEEE International Conference on Systems, Man and Cybernetics, SMC 2004
Y2 - 10 October 2004 through 13 October 2004
ER -