We consider the multistage stochastic programming problem where uncertainty enters the right-hand sides of the problem. Stochastic Dual Dynamic Programming (SDDP) is a popular method to solve such problems under the assumption that the random data process is stagewise independent. There exist two approaches to incorporate dependence into SDDP. One approach is to model the data process as an aut...

Aspect-base Sentiment Analysis is a core component in Review Recommendation System. With the booming of customers’ reviews online, an efficient sentiment analysis algorithm will substantially enhance a review recommendation system’s performance, providing users with more helpful and informative reviews. Recently, two kinds of LDA derived models, namely Word Model and Phrase Model, take the domi...

We define a regularized variant of the Dual Dynamic Programming algorithm called REDDP (REgularized Dual Dynamic Programming) to solve nonlinear dynamic programming equations. We extend the algorithm to solve nonlinear stochastic dynamic programming equations. The corresponding algorithm, called SDDP-REG, can be seen as an extension of a regularization of the Stochastic Dual Dynamic Programming...

Power generation planning in large-scale hydrothermal systems is a complex optimization task, specially due to the high uncertainty in the inflows to hydro plants. Since it is impossible to traverse the huge scenario tree of the multi-stage problem, stochastic dual dynamic programming (SDDP) is the leading optimization technique to solve it, originally from an expected-cost minimization perspec...

Hydro-thermal scheduling is the problem of finding an optimal dispatch of power plants in a system containing both hydro and thermal plants. Since hydro plants are able to store water over long time periods, and since future inflows are uncertain due to precipitation, the resulting multi-stage stochastic optimization problem becomes challenging to solve. Several solution methods have been devel...

In this paper we discuss statistical properties and rates of convergence of the Stochastic Dual Dynamic Programming (SDDP) method applied to multistage linear stochastic programming problems. We assume that the underline data process is stagewise independent and consider the framework where at first a random sample from the original (true) distribution is generated and consequently the SDDP alg...

Risk-averse multistage stochastic programs appear in multiple areas and are challenging to solve. Stochastic Dual Dynamic Programming (SDDP) is a well-known tool address such problems under time-independence assumptions. We show how derive dual formulation for these apply an SDDP algorithm, leading converging deterministic upper bounds risk-averse problems.

Abstract: This paper proposes a robust-optimal trajectory design method for uncertain system to minimize the expected value of objective function. The basic idea is solving Stochastic Differential Dynamic Programming (SDDP), which solve optimal control problem to minimize the expected value of cost-to-go function, with Unscented Transform, which is used to estimate the expected value. Most rece...

When a package is shipped, the customer often requires the delivery to be made within a particular time window or by a deadline. However, meeting such time requirements is difficult, and delivery companies may not always know ahead of time which customers will need a delivery. In this thesis, we present models and solution approaches for two stochastic last-mile delivery problems in which custo...

We prove the almost-sure convergence of a class of samplingbased nested decomposition algorithms for multistage stochastic convex programs in which the stage costs are general convex functions of the decisions, and uncertainty is modelled by a scenario tree. As special cases, our results imply the almost-sure convergence of SDDP, CUPPS and DOASA when applied to problems with general convex cost...