Seminario: “On the Convergence Time of a Natural Dynamics for Linear Programming”

Giovedì 1 Febbraio 2018, ore 12:30 - Aula 2BC30 - Vincenzo Bonifaci


Giovedì 1 Febbraio 2018 alle ore 12:30 in Aula 2BC30, Vincenzo Bonifaci (IASI-CNR, Roma) terrà un seminario dal titolo “On the Convergence Time of a Natural Dynamics for Linear Programming”.

We consider a system of nonlinear ordinary differential equations for the solution of linear programming (LP) problems that was first proposed in the mathematical biology literature as a model for the foraging behavior of acellular slime mold Physarum polycephalum, and more recently considered as a method to solve LPs. We study the convergence time of the continuous Physarum dynamics in the context of the linear programming problem, and derive a new time bound to approximate optimality that depends on the relative entropy between projected versions of the optimal point and of the initial point. The bound scales logarithmically with the LP cost coefficients and linearly with the inverse of the relative accuracy, establishing the efficiency of the dynamics for arbitrary LP instances with positive costs.