Necessary conditions for bilevel dynamic optimization problems
Date
2009-09-10T15:48:36Z
Authors
Ye, Jane J.
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Abstract
In this paper we study the bilevel dynamic optimization problem, which is a hierarchy of two optimization problems where the constraint region of the upper level problem is determined implicitly by the solution to the lower level problem and where the upper level decision variable is a vector while the lower level decision variable is an admissible control function. To obtain optimality conditions, we reformulate the bilevel dynamic optimization problem as a single level optimal control problem which involves the value function of the lower level problem. Sensitivity analysis of the lower level problem with respect to the perturbation in the upper level decision variable is given and first order necessary optimality conditions are derived by using nonsmooth analysis.
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Keywords
necessary conditions, bilevel dynamic optimization problems, sensitivity analysis, nonsmooth analysis, value functions