Dynamic optimization refers to the broad class of optimization or decision-making problems where some problem parameters are uncertain. Everyone including individuals, businesses and even Governments need to solve such decision problems under uncertainty at a regular basis. A commonly used approach is to model the parameter uncertainty using probability distributions (possibly correlated) and formulate the problem as a stochastic optimization problem. While it can be a reasonable approach in many applications, it is by and large computationally intractable. Moreover, quite often we do not have sufficient historical data to estimate the probability distributions to formulate the stochastic optimization problem.
The primary focus of this project is consider different solution paradigms such as robust optimization and affine policies for dynamic optimization problems that are significantly more tractable, and study the relation between these different solution approaches. Such a study would provide significant insights towards developing better and faster algorithms for dynamic optimization problems. The grand goal of the proposed work is to develop a theory of tractable solution approaches for dynamic optimization problems that has a potential of significant impact in many application areas.
Through this project, the PI strives to have a positive impact at various levels that includes (i) developing a deeper theoretical understanding of dynamic optimization that advances the frontier of our knowledge, (ii) the dissemination of research done in this project to the real-world, and (iii) the training of graduate students in research and teaching which is an extremely important link in creating a sustainable cycle of research and its dissemination to practice. The PI intends to actively pursue dynamic optimization problems arising in electricity markets especially due to a broader integration of highly variable renewable sources of power (such as wind and solar) and other factors. The tools and insights developed in this project can have a big impact in this area which is very critical both from an economic as well as climate point of view.
