dynamic programming

In recent years, new technologies in neuroscience have made it possible to measure the activities of large numbers of neurons simultaneously in behaving animals. For each neuron, a fluorescence trace is measured; this can be seen as a first-order approximation of the neuron's activity over time. Determining the exact time at which a neuron spikes on the basis of its fluorescence trace is an important open problem in the field of computational neuroscience.

Classical optimal control problems for (ordinary, stochastic, or evolutionary partial) differential equations have the following feature: When an optimal control is found for a given initial time and initial state, the optimal control will remain optimal as time goes by along the optimal trajectory. This is called the time-consistency of the problem. However, in reality, more than often, the optimal control will hardly stay optimal later on. This is called the time-inconsistency.

Multistage stochastic programming (MSP) is a framework for sequential decision making under uncertainty where the decision space is typically high dimensional and involves complicated constraints, and the uncertainty is modeled by a general stochastic process. In the traditional risk neutral setting, the goal is to find a sequence of decisions or a policy so as to optimize an expected value objective. MSP has found applications in a variety of important sectors including energy, finance, manufacturing, services, and natural resources.