Brian Dandurand – Optimization Online

A Bilevel Approach for Identifying the Worst Contingencies for Nonconvex Alternating Current Power Systems

Published: 2019/07/25, Updated: 2020/06/15

(Mixed) Integer Nonlinear Programming, Branch and Cut Algorithms, Robust Optimization network contingency identification, nonconvex robust optimization, nonlinear mixed-integer programming, optimal power flow

We address the bilevel optimization problem of identifying the most critical attacks to an alternating current (AC) power flow network. The upper-level binary maximization problem consists in choosing an attack that is treated as a parameter in the lower-level defender minimization problem. Instances of the lower-level global minimization problem by themselves are NP-hard due to … Read more

Scalable Branching on Dual Decomposition of Stochastic Mixed-Integer Programming Problems

Published: 2018/10/17, Updated: 2020/02/19

Brian Dandurand

Kibaek Kim

(Mixed) Integer Linear Programming, Parallel Algorithms, Stochastic Programming

We present a scalable branching method for the dual decomposition of stochastic mixed-integer programming. Our new branching method is based on the branching method proposed by Caro e and Schultz that creates branching disjunctions on first-stage variables only. We propose improvements to the process for creating branching disjunctions, including 1) branching on the optimal solutions … Read more

A parallelizable augmented Lagrangian method applied to large-scale non-convex-constrained optimization problems

Published: 2016/11/20

(Mixed) Integer Nonlinear Programming, Constrained Nonlinear Optimization, Parallel Algorithms augmented lagrangian method, nonlinear block gauss-seidel method, parallel computing, proximal bundle method, simplicial decomposition method

We contribute improvements to a Lagrangian dual solution approach applied to large-scale optimization problems whose objective functions are convex, continuously differentiable and possibly nonlinear, while the non-relaxed constraint set is compact but not necessarily convex. Such problems arise, for example, in the split-variable deterministic reformulation of stochastic mixed-integer optimization problems. The dual solution approach needs … Read more

Combining Penalty-based and Gauss-Seidel Methods for solving Stochastic Mixed-Integer Problems

Published: 2016/10/27

Stochastic Programming decomposition, gauss-seidel method, lagrangian duality, penalty-based method, stochastic programming

In this paper, we propose a novel decomposition approach for mixed-integer stochastic programming (SMIP) problems that is inspired by the combination of penalty-based Lagrangian and block Gauss-Seidel methods (PBGS). In this sense, PBGS is developed such that the inherent decomposable structure that SMIPs present can be exploited in a computationally efficient manner. The performance of … Read more

Combining Progressive Hedging with a Frank-Wolfe Method to Compute Lagrangian Dual Bounds in Stochastic Mixed-Integer Programming

Published: 2016/03/30, Updated: 2016/06/14

(Mixed) Integer Linear Programming, Stochastic Programming frank-wolfe, lagrangian duality, mixed-integer stochastic programming, progressive hedging

We present a new primal-dual algorithm for computing the value of the Lagrangian dual of a stochastic mixed-integer program (SMIP) formed by relaxing its nonanticipativity constraints. The algorithm relies on the well-known progressive hedging method, but unlike previous progressive hedging approaches for SMIP, our algorithm can be shown to converge to the optimal Lagrangian dual … Read more

Scenario Set Partition Dual Bounds for Multistage Stochastic Programming: A Hierarchy of Bounds and a Partition Sampling Approach

Published: 2016/01/28, Updated: 2016/12/12

Stochastic Programming stochastic programming

We consider multistage stochastic programming problems in which the random parameters have finite support, leading to optimization over a finite scenario set. We propose a hierarchy of bounds based on partitions of the scenario set into subsets of (nearly) equal cardinality. These expected partition (EP) bounds coincide with EGSO bounds provided by Sandikci et al. … Read more