Dynamic Optimization Problems and Applications

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Recent developments on Stackelberg Games and Incentive Strategies are adapted to develop a novel decomposition approach for the solution of dynamic optimization problems. The approach involves stage-wise decomposition, and stems from the following observation: "In the dynamic programming approach to optimization, if the cost-to-go functions at every stage were known, then the solution of an N-stage optimal control problem would be obtained by solving (in parallel) N decoupled static (single stage) optimization problems." Taking this observation as a starting point, the principal investigators suggest that even if the optimal cost-to-go functions are not known, one can start with some initial guesses, solve the corresponding N static optimization problems, update on the initial guesses using these solutions, solve a new set of optimization problems,...and so on..., until some convergence is achieved. The research is to study various aspects of this scheme, including its convergence properties, computational requirements, and feasibility, and apply it to an economic dispatch problem arising in power systems.