Nonlinear neural networks for solving the shortest path problem (Q2381352)

The shortest path problem is reduced to the linear programming problem (LPP) in the spirit of \textit{M.~S.~Bazaraa, J.~J.~Jarvis} and \textit{H.~D.~Sherali} [Linear programming and network flows. 2nd ed. (John Wiley and Sons, New York etc) (1990; Zbl 0722.90042); 3rd ed. (2005; Zbl 1061.90085)]. Then the authors construct two reductions of LPPs to neural network models. The first one is constructed like the one of \textit{S.~Effati} and \textit{M.~Bayman} [Appl.\ Math.\ Comput.\ 168, No.~2, 1370--1379 (2005; Zbl 1081.65054)]. An second one is inherently a sequential application of the penalty method and the gradient projection method to the LPP. An illustrative example is given.