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 LP instances. 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.

Bonifaci, V. (2017). On the convergence time of a natural dynamics for linear programming. In Proc. of the 28th Int. Symposium on Algorithms and Computation. Dagstuhl : Schloss Dagstuhl- Leibniz-Zentrum fur Informatik [10.4230/LIPIcs.ISAAC.2017.17].

On the convergence time of a natural dynamics for linear programming

Bonifaci V.
2017

Abstract

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 LP instances. 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.
Bonifaci, V. (2017). On the convergence time of a natural dynamics for linear programming. In Proc. of the 28th Int. Symposium on Algorithms and Computation. Dagstuhl : Schloss Dagstuhl- Leibniz-Zentrum fur Informatik [10.4230/LIPIcs.ISAAC.2017.17].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11590/381899
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