Optimal Strategies for Bilevel Dynamic Problems∗
نویسنده
چکیده
In this paper we study the bilevel dynamic problem, which is a hierarchy of two dynamic optimization problems, where the constraint region of the upper level problem is determined implicitly by the solutions to the lower level optimal control problem. To obtain optimality conditions, we reformulate the bilevel dynamic problem as a single level optimal control problem that 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. A constraint qualification of calmness type and a sufficient condition for the calmness are also given.
منابع مشابه
A new method for solving fully fuzzy linear Bilevel programming problems
In this paper, a new method is proposed to find the fuzzy optimal solution of fully fuzzy linear Bilevel programming (FFLBLP) problems by representing all the parameters as triangular fuzzy numbers. In the proposed method, the given FFLBLP problem is decomposed into three crisp linear programming (CLP) problems with bounded variables constraints, the three CLP problems are solved separately...
متن کاملA New Approach for Solving Fully Fuzzy Bilevel Linear Programming Problems
This paper addresses a type of fully fuzzy bilevel linear programming (FFBLP) wherein all the coefficients and decision variables in both the objective function and constraints are triangular fuzzy numbers. This paper proposes a new simple-structured, efficient method for FFBLP problems based on crisp bilevel programming that yields fuzzy optimal solutions with unconstraint variables and parame...
متن کاملRobust Optimization of Dynamic Systems
This thesis is about robust optimization, a class of mathematical optimization problems which arise frequently in engineering applications, where unknown process parameters and unpredictable external influences are present. Especially, if the uncertainty enters via a nonlinear differential equation, the associated robust counterpart problems are challenging to solve. The aim of this thesis is t...
متن کاملSimulated Annealing Approach for Solving Bilevel Programming Problem
Bilevel programming, a tool for modeling decentralized decision problems, consists of the objective of the leader at its first level and that of the follower at the second level. Bilevel programming has been proved to be an Np-hard problem. Numerous algorithms have been developed for solving bilevel programming problems. These algorithms lack the required efficiency for solving a real problem. ...
متن کاملFinding optimal strategies in a multi-period multi-leader-follower Stackelberg game using an evolutionary algorithm
Stackelberg games are a classic example of bilevel optimization problems, which are often encountered in game theory and economics. These are complex problems with a hierarchical structure, where one optimization task is nested within the other. Despite a number of studies on handling bilevel optimization problems, these problems still remain a challenging territory, and existing methodologies ...
متن کامل