The automated real time control of an electrical network is achieved through the estimation of its state using Phasor Measurement Units (PMUs). Given an undirected graph representing the network, we study the problem of finding the minimum number of PMUs to place on the edges such that the graph is fully observed. This problem is … Read more
In this paper, we consider the control problem with the Average-Value-at-Risk (AVaR) criteria of the possibly unbounded $L^{1}$-costs in infinite horizon on a Markov Decision Process (MDP). With a suitable state aggregation and by choosing a priori a global variable $s$ heuristically, we show that there exist optimal policies for the infinite horizon problem. To … Read more
We consider an n-player finite strategic game. The payoff vector of each player is a random vector whose distribution is not completely known. We assume that the distribution of a random payoff vector of each player belongs to a distributional uncertainty set. We define a distributionally robust chance-constrained game using worst-case chance constraint. We consider … Read more
Stability analysis for optimization problems with chance constraints concerns impact of variation of probability measure in the chance constraints on the optimal value and optimal solutions and research on the topic has been well documented in the literature of stochastic programming. In this paper, we extend such analysis to optimization problems with distributionally robust chance … Read more
We study two-stage stochastic mixed integer programs (TSS-MIPs) with integer variables in the second stage. We show that under suitable conditions, the second stage MIPs can be convexified by adding parametric cuts a priori. As special cases, we extend the results of Miller and Wolsey (Math Program 98(1):73-88, 2003) to TSS-MIPs. Furthermore, we consider second … Read more
We present a branch-and-bound framework to solve the following problem: Given a graph G and an integer k, find a subgraph of G formed by removing no more than k edges that contains the most symmetry. We call symmetries on such a subgraph “almost symmetries” of G. We implement our branch-and-bound framework in PEBBL to … Read more
In this paper we consider a particular method of clustering for graphs, namely the modularity density maximization. We propose a hierarchical divisive heuristic which works by splitting recursively a cluster into two new clusters by maximizing the modularity density, and we derive four reformulations for the mathematical programming model used to obtain the optimal splitting. … Read more
In many real-world transportation systems, passengers are often required to make a number of interchanges between different modes of transport. As cities continue to grow, a greater number of these connections tend to occur within centrally located Transport Hubs. In order to encourage the uptake of public transport in major cities, it is important for … Read more
As shown in [9, 1], signals whose wavelet coefficients exhibit a rooted tree structure can be recovered — using specially-adapted compressed sensing algorithms — from just $n=\mathcal{O}(k)$ measurements, where $k$ is the sparsity of the signal. Motivated by these results, we introduce a simplified proportional-dimensional asymptotic framework which enables the quantitative evaluation of recovery guarantees … Read more
This paper describes an accelerated HPE-type method based on general Bregman distances for solving monotone saddle-point (SP) problems. The algorithm is a special instance of a non-Euclidean hybrid proximal extragradient framework introduced by Svaiter and Solodov [28] where the prox sub-inclusions are solved using an accelerated gradient method. It generalizes the accelerated HPE algorithm presented … Read more