52 citations · 216 across the 27 of their papers we have counts for
22 papers · 1 filter
On a Computationally Ill-Behaved Bilevel Problem with a Continuous and Nonconvex Lower Level
Yasmine Beck, Daniel Bienstock, Martin Schmidt +1
It is well known that bilevel optimization problems are hard to solve both in theory and practice. In this paper, we highlight a further computational difficulty when it comes to s…
Cardinality Minimization, Constraints, and Regularization: A Survey
Andreas M. Tillmann, Daniel Bienstock, Andrea Lodi +1
We survey optimization problems that involve the cardinality of variable vectors in constraints or the objective function. We provide a unified viewpoint on the general problem cla…
Complexity, Exactness, and Rationality in Polynomial Optimization
Daniel Bienstock, Alberto del Pia, Robert Hildebrand
We focus on rational solutions or nearly-feasible rational solutions that serve as certificates of feasibility for polynomial optimization problems. We show that, under some separa…
Mathematical Programming formulations for the Alternating Current Optimal Power Flow problem
Daniel Bienstock, Mauro Escobar, Claudio Gentile +1
Power flow refers to the injection of power on the lines of an electrical grid, so that all the injections at the nodes form a consistent flow within the network. Optimality, in th…
Stochastic defense against complex grid attacks
Daniel Bienstock, Mauro Escobar
We describe defense mechanisms designed to detect sophisticated grid attacks involving both physical actions (including load modification) and sensor output alteration, with the la…
Simpler derivation of bounded pitch inequalities for set covering, and minimum knapsack sets
Daniel Bienstock, Mark Zuckerberg
A valid inequality α^Tx \ge α_0 for a set covering problem is said to have pitch <= k ( a positive integer) if the k smallest positive α_j sum to at least alpha_0. This paper prese…
Variance-Aware Optimal Power Flow
Daniel Bienstock, Apurv Shukla
The incorporation of stochastic loads and generation into the operation of power grids gives rise to an exposure to stochastic risk. This risk has been addressed in prior work thro…
Robust linear control of nonconvex battery operation in transmission systems
Daniel Bienstock, Carsten Matke, Gonzalo Munoz +1
We describe a robust multiperiod transmission plan- ning model including renewables and batteries, where battery output is used to partly offset renewable output deviations from fo…
Outer-Product-Free Sets for Polynomial Optimization and Oracle-Based Cuts
Daniel Bienstock, Chen Chen, Gonzalo Muñoz
This paper introduces cutting planes that involve minimal structural assumptions, enabling the generation of strong polyhedral relaxations for a broad class of problems. We conside…
Strong NP-hardness of AC power flows feasibility
Daniel Bienstock, Abhinav Verma
We present a rigorous proof of strong NP-hardness of the AC-OPF problem.
Models for managing the impact of an epidemic
Daniel Bienstock, A. Cecilia Zenteno
In this paper we consider robust models for emergency staff deployment in the event of a flu pandemic. We focus on managing critical staff levels at organizations that must remain…
Two-sided linear chance constraints and extensions
Miles Lubin, Daniel Bienstock, Juan Pablo Vielma
We examine the convexity and tractability of the two-sided linear chance constraint model under Gaussian uncertainty. We show that these constraints can be applied directly to mode…
Robust Control of Cascading Power Grid Failures using Stochastic Approximation
Daniel Bienstock, Guy Grebla
Cascading failure of a power transmission system are initiated by an exogenous event that disable a set of elements (e.g., lines) followed by a sequence of interrelated failures (o…
Vulnerability Analysis of Power Systems
Taedong Kim, Stephen J. Wright, Daniel Bienstock +1
Potential vulnerabilities in a power grid can be exposed by identifying those transmission lines on which attacks (in the form of interference with their transmission capabilities)…
LP approximations to mixed-integer polynomial optimization problems
Daniel Bienstock, Gonzalo Munoz
We present a class of linear programming approximations for constrained optimization problems. In the case of mixed-integer polynomial optimization problems, if the intersection gr…
On linear relaxations of OPF problems
Daniel Bienstock, Gonzalo Munoz
We present lifted linear relaxations of the OPF problem.
A note on polynomial solvability of the CDT problem
Daniel Bienstock
We describe a simple polynomial-time algorithm for the CDT problem that relies on a construction of Barvinok.
Synchronization-Aware and Algorithm-Efficient Chance Constrained Optimal Power Flow
Russell Bent, Daniel Bienstock, Michael Chertkov
One of the most common control decisions faced by power system operators is the question of how to dispatch generation to meet demand for power. This is a complex optimization prob…
Chance Constrained Optimal Power Flow: Risk-Aware Network Control under Uncertainty
Daniel Bienstock, Michael Chertkov, Sean Harnett
When uncontrollable resources fluctuate, Optimum Power Flow (OPF), routinely used by the electric power industry to re-dispatch hourly controllable generation (coal, gas and hydro…
Optimizing convex functions over nonconvex sets
Daniel Bienstock, Alexander Michalka
In this paper we derive strong linear inequalities for sets of the form {(x, q) \in Rd \times R : q \geq Q(x), x \in Rd - int(P)}, where Q(x) : Rd \rightarrow R is a quadratic func…
Optimal adaptive control of cascading power grid failures
Daniel Bienstock
We present theoretical results and experiments with parallel algorithms for computing an adaptive, online control with the objective of attenuating a power grid cascading failure.
The N-K Problem in Power Grids: New Models, Formulations and Numerical Experiments (extended version)
Daniel Bienstock, Abhinav Verma
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 ask…