This paper studies the multi-stage real-time stochastic operation of grid-tied multi-energy microgrids (MEMGs) via the hybrid model predictive control (MPC) and approximate dynamic programming (ADP) approach. In the MEMG, practical power and thermal network constraints, heterogeneous energy storage devices, and distributed generations are involved. Given the relatively large thermal inertia and slow thermal energy fluctuation, only uncertainties of renewable energy sources and active/reactive power loads are considered. Then, historical data are adopted as training scenarios for the MPC-ADP method to acquire empirical knowledge for dealing with all the diverse uncertainties. Further, piecewise linear functions are used to approximate value functions with respect to the operation status of energy storage assets, which enables sequentially solving the Bellman’s equation forward through time to minimize MEMG operation cost. Finally, numerical case studies are conducted to illustrate the effectiveness and superiority of the proposed MPC-ADP approach. Simulation results indicate that with sufficient information embedded, the MPC-ADP approach could obtain good-enough real-time operation solutions with the successively updated forecast. Further, it outperforms alternative real-time operation benchmarks in terms of optimality and convergence for various application scenarios.

Developing marketing campaigns for a new product or a new target population is challenging because of the scarcity of relevant historical data. Building on dynamic Bayesian learning, a sequential optimization assists in creating new data points within a finite number of learning phases. This procedure identifies effective advertisement design elements as well as customer segments that maximize the expected outcome of the final marketing campaign. In this paper, the marketing campaign performance is modeled by a multiplicative advertising exposure model with Poisson arrivals. The intensity of the Poisson process is a function of the marketing campaign features. A forward-looking measurement policy is formulated to maximize the expected improvement in the value of information in each learning phase. A computationally efficient approach is proposed that consists of solving a sequence of mixed-integer linear optimization problems. The performance of the optimal learning policy over a set of benchmark policies is evaluated using examples inspired from the property and casualty insurance industry. Further extensions of the model are discussed. This paper was accepted by Eric Anderson, marketing.

This paper proposes an approach to compute the implied transition matrices from observations of market data on financial derivatives, when the price of the underlying originates from a structural model and the payoffs are received over a period of time. The structural price model involves a price formation mechanism which computes the price based on a set of Markovian inputs and constrained optimization processes. The developed inference method relies on a linear description of the derivative values in terms of occupation measures of the payoff duration. We establish closed-form expressions between occupation measures and state transitions, which then enable us to characterize implied state transition probabilities consistent with the market data on the derivative values. We develop methods to solve the optimization problem with the resulting nonlinear occupation measure equation. Numerical illustrations of the approach are presented for financial derivatives on network capacities. By applying the method to an electric network, we investigate the relation between financial transmission correct contract values and a range of implied probabilities of congestion in the network.