The approximation of stochastic processes by trees is an important topic in multistage stochastic programming. In this paper we focus on improving the approximation of large trees by smaller (tractable) trees. The quality of the approximation is measured by the nested distance, recently introduced in [Pflug]. The nested distance is derived from the Wasserstein distance. … Read more
We prove that uniform second order growth, tilt stability, and strong metric regularity of the subdifferential — three notions that have appeared in entirely different settings — are all essentially equivalent for any lower-semicontinuous, extended-real-valued function. CitationCornell University, School of Operations Research and Information Engineering, 206 Rhodes Hall Cornell University Ithaca, NY 14853. May 2012.ArticleDownload … Read more
We consider a class of linear programs involving a set of covering constraints of which at most k are allowed to be violated. We show that this covering linear program with violation is strongly NP-hard. In order to improve the performance of mixed-integer programming (MIP) based schemes for these problems, we introduce and analyze a … Read more
We consider two game-theoretic models of the generation capacity expansion problem in liberalized electricity markets. The first is an open loop equilibrium model, where generation companies simultaneously choose capacities and quantities to maximize their individual profit. The second is a closed loop model, in which companies first choose capacities maximizing their profit anticipating the market … Read more
In this paper we survey some important classes of gap function for variational inequalities and also some recently introduced gap functions for generalized variational inequalities. A new gap function is proposed for generalized variational inequalities and error bound is developed. Error bounds are also developed for some particular classes of gap functions. In fact a … Read more
We analyze the relationship between the noise level of a function and the accuracy and reliability of derivatives and difference estimates. We derive and empirically validate measures of quality for both derivatives and difference estimates. Using these measures, we quantify the accuracy of derivatives and differences in terms of the noise level of the function. … Read more
This short article analyzes an interesting property of the Bregman iterative procedure, which is equivalent to the augmented Lagrangian method after a change of variable, for minimizing a convex piece-wise linear function J(x) subject to linear constraints Ax=b. The procedure obtains its solution by solving a sequence of unconstrained subproblems of minimizing J(x)+1/2||Ax-b^k||^2, where b^k … Read more
We consider cooperative traveling salesman games with non-negative asymmetric costs satisfying the triangle inequality. We construct a stable cost allocation with budget balance guarantee equal to the Held-Karp integrality gap for the asymmetric traveling salesman problem, using the parsimonious property and a previously unknown connection to linear production games. We also show that our techniques … Read more
A novel approach for obtaining globally optimal solutions to design of networks with nonlinear resistances and potential driven flows is proposed. The approach is applicable to networks where the potential loss on an edge in the network is governed by a convex and strictly monotonically increasing function of flow rate. We introduce a relaxation of … Read more
We present a new barrier-based method of constructing smoothing approximations for the Euclidean projector onto closed convex cones. These smoothing approximations are used in a smoothing proximal point algorithm to solve monotone nonlinear complementarity problems (NCPs) over a convex cones via the normal map equation. The smoothing approximations allow for the solution of the smoothed … Read more