Based on a preconditioned version of the randomized block-coordinate forward-backward algorithm recently proposed in [Combettes,Pesquet,2014], several variants of block-coordinate primal-dual algorithms are designed in order to solve a wide array of monotone inclusion problems. These methods rely on a sweep of blocks of variables which are activated at each iteration according to a random rule, … Read more
In this paper we discuss stochastic optimal path problems where the goal is to find a path that has minimal expected cost and at the same time is less risky (in terms of travel time) than a given benchmark path. The model is suitable for a risk-averse traveler, who prefers a path with a more … Read more
The growth-optimal portfolio is designed to have maximum expected log-return over the next rebalancing period. Thus, it can be computed with relative ease by solving a static optimization problem. The growth-optimal portfolio has sparked fascination among finance professionals and researchers because it can be shown to outperform any other portfolio with probability 1 in the … Read more
Unit commitment decisions made in the day-ahead market and during subsequent reliability assessments are critically based on forecasts of load. Traditional, deterministic unit commitment is based on point or expectation-based load forecasts. In contrast, stochastic unit commitment relies on multiple load scenarios, with associated probabilities, that in aggregate capture the range of likely load time-series. … Read more
In this second portion of a two-part analysis of a scalable computational approach to stochastic unit commitment, we focus on solving stochastic mixed-integer programs in tractable run-times. Our solution technique is based on Rockafellar and Wets’ progressive hedging algorithm, a scenario-based decomposition strategy for solving stochastic programs. To achieve high-quality solutions in tractable run-times, we … Read more
We consider a reliable network design problem under uncertain edge failures. Our goal is to select a minimum-cost subset of edges in the network to connect multiple terminals together with high probability. This problem can be seen as a stochastic variant of the Steiner tree problem. We propose a scenario-based Steiner cut formulation, and a … Read more
We consider the integer L-shaped method for two-stage stochastic integer programs. To improve the performance of the algorithm, we present and combine two strategies. First, to avoid time-consuming exact evaluations of the second-stage cost function, we propose a simple modification that alternates between linear and mixed-integer subproblems. Then, to better approximate the shape of the … Read more
This work investigates the properties of stochastic quasi-Fejér monotone sequences in Hilbert spaces and emphasizes their pertinence in the study of the convergence of block-coordinate fixed point methods. The iterative methods under investigation feature random sweeping rules to select the blocks of variables that are activated over the course of the iterations and allow for … Read more
Sample-average approximations (SAA) are a practical means of finding approximate solutions of stochastic programming problems involving an extremely large (or infinite) number of scenarios. SAA can also be used to find estimates of a lower bound on the optimal objective value of the true problem which, when coupled with an upper bound, provides confidence intervals … Read more
In this paper, we study chance constrained mixed integer program with consideration of recourse decisions and their incurred cost, developed on a finite discrete scenario set. Through studying a non-traditional bilinear mixed integer formulation, we derive its linear counterparts and show that they could be stronger than existing linear formulations. We also develop a variant … Read more