A note on polynomial solvability of the CDT problem
We describe a simple polynomial-time algorithm for the CDT problems that relies on a construction of Barvinok. CitationColumbia UniversityArticleDownload View PDF
Daniel Bienstock
Approximation Algorithms for the Incremental Knapsack Problem via Disjunctive Programming
In the \emph{incremental knapsack problem} ($\IK$), we are given a knapsack whose capacity grows weakly as a function of time. There is a time horizon of $T$ periods and the capacity of the knapsack is $B_t$ in period $t$ for $t = 1, \ldots, T$. We are also given a set $S$ of $N$ items … Read more
Polynomial solvability of variants of the trust-region subproblem
The trust region subproblem concerns the minimization of a general quadratic over the unit ball in R^n. Extensions to this problem are of interest because of applications to, for example, combinatorial optimization. However the extension obtained by adding an arbitrary family of linear side constraints is NP-hard. In this paper we consider variants of the … Read more
Cutting-planes for optimization of convex functions over nonconvex sets
Motivated by mixed-integer, nonlinear optimization problems, we derive linear inequality characterizations for sets of the form conv{(x, q ) \in R^d × R : q \in Q(x), x \in R^d – int(P )} where Q is convex and differentiable and P \subset R^d . We show that in several cases our characterization leads to polynomial-time … Read more
Models for managing the impact of an epidemic
In this paper we consider robust models of surge capacity plans to be deployed in the event of a flu pandemic. In particular, we focus on managing critical staff levels at organizations that must remain operational during such an event. We develop efficient procedures for managing emergency resources so as to minimize the impact of … Read more
Strong formulations for convex functions over nonconvex sets
In this paper we derive strong linear inequalities for sets of the form {(x, q) ∈ R^d × R : q ≥ Q(x), x ∈ R^d − int(P ) }, where Q(x) : R^d → R is a quadratic function, P ⊂ R^d and “int” denotes interior. Of particular but not exclusive interest is the … Read more
Optimal adaptive control of cascading power grid failures
We describe experiments with parallel algorithms for computing adaptive controls for attenuating power grid cascading failures. CitationColumbia University, 2010ArticleDownload View PDF
A new LP algorithm for precedence constrained production scheduling
We present a number of new algorithmic ideas for solving LP relaxations of extremely large precedence constrained production scheduling problems. These ideas are used to develop an implementation that is tested on a variety of real-life, large scale instances; yielding optimal solutions in very practicable CPU time. CitationUnpublished. Columbia University, BHP Billiton, August 2009.ArticleDownload View … Read more
Eigenvalue techniques for proving bounds for convex objective, nonconvex programs
We describe techniques combining the S-lemma and computation of projected quadratics which experimentally yield strong bounds on the value of convex quadratic programs with nonconvex constraints Citationunpublished report, Columbia University, March 2009ArticleDownload View PDF
The N – k Problem in Power Grids: New Models, Formulations and Computation
Given a power grid modeled by a network together with equations describing the power flows, power generation and consumption, and the laws of physics, the so-called N – k problem asks whether there exists a set of k or fewer arcs whose removal will cause the system to fail. We present theoretical results and computation … Read more