Question

How does a dynamic optimality condition differ from a static optimality conditions

Answer 1

Dynamic optimality condition

Dynamic traffic assignment model is nonconvex mathematical program and nonlinear. optimality conditions necessary require equalization of certain marginal costs for all the paths that are being used, and these optimality conditions are shown to be a generalization of the optimality conditions of a static conventional traffic assignment problem.

Static optimality condition

The equivalent static loads method) ESLM) is a optimization structural method. This method defines two separate domains: the analysis domain and design domain.

Analysis is performed in the analysis domain, equivalent static loads (ESLs) sets are generated linear static optimization response is carried out in the design domain using the ESLs and the process iterates until the criteria stopping are satisfied. This method is quite popular and some commercial systems have installed the method.

Theoretical foundation of ESLM by park and Kang was validated for linear dynamic response optimization. They claimed that when the ESLM process terminates, the optimum satisfies solution the Karush-Kuhn-Tucker (KKT) necessary condition. Some critical issues raised by stolpe. He showed that the theoretical results in Park and Kang are not valid. In this paper, the process validation of Park and Kang is amended according to the Stolpe’s corrections. It is shown that the original claim for thecondition(kkt) is valid by adding some mathematical aspects.