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This paper focuses on the development of optimality conditions for a bilevel optimal control problem with pure state constrains in the upper level and a finite-dimensional parametric optimization problem in the lower level. After transforming the problem into an equivalent single-level problem we concentrate on the derivation of a necessary optimality condition of Pontryagin-type. We point out some major difficulties arising from the bilevel structure of the original problem and its pure state constraints in the upper level leading to a degenerated maximum principle in the absence of constraint qualifications. Hence, we use a partial penalization approach and a well-known regularity condition for optimal control problems with pure state constraints to ensure the non-degeneracy of the derived maximum principle. Finally, we illustrate the applicability of the derived theory by means of a small example.

Routing games are amongst the most well studied domains of game theory. How relevant are these pen-and-paper calculations to understanding the reality of everyday traffic routing? We focus on a semantically rich dataset that captures detailed information about the daily behavior of thousands of Singaporean commuters and examine the following basic questions:-Does the traffic equilibrate? -Is the system behavior consistent with latency minimizing agents? -Is the resulting system efficient?In order to capture the efficiency of the traffic network in a way that agrees with our everyday intuition we introduce a new metric, the stress of catastrophe, which reflects the combined inefficiencies of both tragedy of the commons as well as price of anarchy effects.

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In this paper we discuss special bilevel optimal control problems where the upper level problem is an optimal control problem of ODEs with control and terminal constraints and the lower level problem is a finite-dimensional parametric optimization problem where the parameter is the final state of the state variable of the upper level. We tackle this problem using tools of nonsmooth analysis, optimization in Banach spaces and bilevel programming to derive a necessary optimality condition of linearized Pontryagin-type.

This article investigates the geographical spread of confirmed COVID-19 cases and deaths across municipalities in Mexico. It focuses on the spread dynamics and containment of the virus between Phase I (from March 23 to May 31, 2020) and Phase II (from June 1 to August 22, 2020) of the social distancing measures. It also examines municipal-level factors associated with cumulative COVID-19 cases and deaths to understand the spatial determinants of the pandemic. The analysis of the geographic pattern of the pandemic via spatial scan statistics revealed a fast spread among municipalities. During Phase I, clusters of infections and deaths were mainly located at the country’s center, whereas in Phase II, these clusters dispersed to the rest of the country. The regression results from the zero-inflated negative binomial regression analysis suggested that income inequality, the prevalence of obesity and diabetes, and concentration of fine particulate matter (PM 2.5) are strongly positively associated with confirmed cases and deaths regardless of lockdown.