Time-varying linear programming via LVI-PDNN with numerical examples

Playing a fundamental role in mathematic optimization, linear programming (LP) problems have been widely encountered in various scientific disciplines and industrial applications. Although static LP problems have been investigated extensively and applied to abundant scientific fields through the last decades, researches concerning time-varying linear programming (TVLP) problem solving are in relatively small amount. In this paper, the TVLP problems are solved by a linear-variational-inequality based primal-dual neural network (LVI-PDNN), which is originally designed for static LP problem solving. Numerical examples and computer simulations further reveal that LVI-PDNN could approach the theoretical solution when solving TVLP problems subject to equality, inequality and bound constraints simultaneously.