Abstract We study planar polygonal curves with the variational methods. show a unified interpretation of discrete curvatures and Steiner-type formula by extracting notion curvature vector from first variation length functional. Moreover, we determine equilibrium for functional under area-constraint condition their stability.

Introduction . The article formulates the problems statement about equilibrium states in model of a generalized transport system city, consisting street and road network, centers mass gravity, places residence people, vehicles, as well users themselves, including passengers. solution these makes it possible to identify distributions elements over various subsets (a subset network; center gravit...

Inspired by the optimal value approach, we propose a new reformulation of the optimistic Bilevel programming Problem (BP) as a suitable Generalized Nash Equilibrium Problem (GNEP). We provide a complete analysis of the relationship between the original hierarchical BP and the corresponding “more democratic” GNEP. Moreover, we investigate solvability and convexity issues of our reformulation. Fi...