We consider the incorporation of a time-consistent coherent risk measure into a multi-stage stochastic programming model, so that the model can be solved using a SDDP-type algorithm. We describe the implementation of this algorithm, and study the solutions it gives for an application of hydro-thermal scheduling in the New Zealand electricity system. The performance of … Read more
We describe experiments with parallel algorithms for computing adaptive controls for attenuating power grid cascading failures. CitationColumbia University, 2010ArticleDownload View PDF
When solving nonlinear least-squares problems, it is often useful to regularize the problem using a quadratic term, a practice which is especially common in applications arising in inverse calculations. A solution method derived from a trust-region Gauss-Newton algorithm is analyzed for such applications, where, contrary to the standard algorithm, the least-squares subproblem solved at each … Read more
We investigate cost-sharing mechanisms for scheduling cost-sharing games. We assume that the demand is general—that is, each player can be allocated one of several levels of service. We show how to design mechanisms for these games that are weakly group strategyproof, approximately budget-balanced, and approximately efficient, using approximation algorithms for the underlying scheduling problems. We … Read more
We address an optimization problem in which two agents, each with a set of weighted items, compete in order to minimize the total weight of their solution sets. The latter are built according to a sequential game consisting in a fixed number of rounds. In every round each agent submits one item that may be … Read more
We employ recent work on computational noise to obtain near-optimal finite difference estimates of the derivatives of a noisy function. Our analysis employs a stochastic model of the noise without assuming a specific form of distribution. We use this model to derive theoretical bounds for the errors in the difference estimates and obtain an easily … Read more
We present explicit optimality conditions for a nonsmooth functional defined over the (properly or weakly) Pareto set associated to a multiobjective linear-quadratic control problem. This problem is very difficult even in a finite dimensional setting, i.e. when, instead of a control problem, we deal with a mathematical programming problem. Amongst different applications, our problem may … Read more
In this paper we introduce robust and stochastically weighted sum approaches to deterministic and stochastic multi-objective optimization. The robust weighted sum approach minimizes the worst case weighted sum of objectives over a given weight region. We study the reformulations of the robust weighted sum problem under different definitions of deterministic weight regions. We next introduce … Read more
Purpose: Iterative projection reconstruction algorithms are currently the preferred reconstruction method in proton computed tomography (pCT). However, due to inconsistencies in the measured data arising from proton energy straggling and multiple Coulomb scattering, noise in the reconstructed image increases with successive iterations. In the current work, we investigated the use of total variation superiorization (TVS) … Read more
We present a game-theoretical dynamic model for competitive electricity markets.We demonstrate that the model can be used to systematically analyze the effects of ramp constraints, initial conditions, dynamic disturbances, forecast horizon, bidding frequency, and some other factors on the price signals.We illustrate the capabilities of the model using a numerical case study ArticleDownload View PDF