Markov Chain Sampling of Hidden Relay States for Economic Dispatch with Cascading Failures

Independent system operators (ISO) of electric power networks aim to dispatch electricity economically while maintaining system reliability. NERC (North America Electric Reliability Council) requires the transmission network to be (N-1)-secure, i.e., to have sufficient supply to satisfy demand in the event of the failure of any single resource in the network. Such a policy is … Read more

Are Weaker Stationarity Concepts of Stochastic MPCC Problems Significant in Absence of SMPCC-LICQ?

In this article, we study weak stationarity conditions (A- and C-) for a particular class of degenerate stochastic mathematical programming problems with complementarity constraints (SMPCC, for short). Importance of the weak stationarity concepts in absence of SMPCC-LICQ are presented through toy problems in which the point of local or global minimum are weak stationary points … Read more

Large Deviation Bounds for Markov Chain Sample Average Approximation via Weak Convergence

A common approach to solve stochastic optimization problems with expectations is to replace the expectations by its sample averages. Large sample asymptotic properties of this approximation are well studied when the sample is i.i.d. In many cases, however, i.i.d. samples are not readily available. On the contrary, one can generate a Harris recurrent Markov chain … Read more

Epi-convergence of Sample Averages of a Random Lower Semi-continuous Functional Generated by a Markov Chain and Application to Stochastic Optimization

The purpose of this article is to establish epigraphical convergence of the sample averages of a random lower semi-continuous functional associated with a Harris recurrent Markov chain with stationary distribution $\pi$. Sample averages associated with an ergodic Markov chain with stationary probability distribution will epigraphically converge from $\pi$-almost all starting points. The property of Harris … Read more