We consider multistage stochastic optimization models containing nonconvex constraints, e.g., due to logical or integrality requirements. We study three variants of Lagrangian relaxations and of the corresponding decomposition schemes, namely, scenario, nodal and geographical decomposition. Based on convex equivalents for the Lagrangian duals, we compare the duality gaps for these decomposition...

An airline’s operational disruptions can lead to flight delays that in turn impact passengers, not only through the delays themselves but also through possible missed connections. Since the length of a delay is often not known in advance, we consider preemptive rerouting of airline passengers before the length of the delay is realized. Our goal is to reaccommodate passengers proactively as soon...

The population growth, is increase in the number of individuals in population and it depends on some random environment effects. There are several different mathematical models for population growth. These models are suitable tool to predict future population growth. One of these models is logistic model. In this paper, by using Feynman-Kac formula, the Adomian decomposition method is applied to ...

Abstract A physical stochastic parameterization is adopted in this work to account for the effects of unresolved small-scale on large-scale flow dynamics. This random model based a transport principle, which ensures strong energy conservation. The dynamic mode decomposition (DMD) performed high-resolution data learn basis velocity field, expressed. Time-harmonic property DMD modes allows us per...

Two-Stage Problems with Stochastic Order Constraints. Darinka Dentcheva, Department of Mathematical Science, Stevens Institute of Technology. Abstract: We consider two-stage risk-averse stochastic optimization problems with a stochastic-order constraint on the second stage decisions. The usual stochastic order, the increasing convex order and a multivariate stochastic order will be discussed. W...

Decomposition has proved to be one of the more effective tools for the solution of large-scale problems, especially those arising in stochastic programming. A decomposition method with wide applicability is Benders’ decomposition, and has been applied to both stochastic programming, as well as integer programming problems. However, this method of decomposition relies on convexity of the value f...

A new stochastic subspace identification algorithm is developed with the help of a stochastic realization on a finite interval. First, a finite-interval realization algorithm is rederived via “block-LDL decomposition” for a finite string of complete covariance sequence. Next, a stochastic subspace identification method is derived by adapting the finiteinterval realization algorithm to incomplet...

This technical note presents explicit formulas for calculating the response moments of stochastic systems by polynomial dimensional decomposition entailing independent random input with arbitrary probability measures. The numerical results indicate that the formulas provide accurate, convergent, and computationally efficient estimates of the second-moment properties. DOI: 10.1061/ ASCE EM.1943-...