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The state of numerical computing is currently characterized by a divide between highly efficient yet typically cumbersome low-level languages such as C, C++, and Fortran and highly expressive yet typically slow high-level languages such as Python and MATLAB. This paper explores how Julia, a modern programming language for numerical computing which claims to… (More)

We present a scalable approach and implementation for solving stochastic programming problems, with application to the optimization of complex energy systems under uncertainty. Stochastic programming is used to make decisions in the present while incorporating a model of uncertainty about future events (scenarios). These problems present serious… (More)

We present a novel approach for solving dense saddle-point linear systems in a distributed-memory environment. This work is motivated by an application in stochastic optimization problems with recourse, but the proposed approach can be used for a large family of dense saddle-point systems, in particular those arising in convex programming. Although… (More)

Preprint ANL/MCS-P3037-0912 For stochastic mixed-integer programs, we revisit the dual decomposition algorithm of Carøe and Schultz from a computational perspective with the aim of its parallelization. We address an important bottleneck of parallel execution by identifying a formulation that permits the parallel solution of the master program by using… (More)

JuMP is an open-source modeling language that allows users to express a wide range of optimization problems (linear, mixed-integer, quadratic, conic-quadratic, and nonlinear) in a high-level, algebraic syntax. JuMP takes advantage of advanced features of the Julia programming language to achieve performance on par with commercial modeling tools. In this… (More)

We present a scalable approach and implementation for solving stochastic optimization problems on high-performance computers. In this work we revisit the sparse linear algebra computations of the parallel solver PIPS with the goal of improving the shared-memory performance and decreasing the time to solution. These computations consist of solving sparse… (More)

We present scalable algebraic modeling software, StochJuMP, for stochastic optimization as applied to power grid economic dispatch. It enables the user to express the problem in a high-level algebraic format with minimal boilerplate. StochJuMP allows efficient parallel model instantiation across nodes and efficient data localization. Computational results… (More)

- Dimitris Bertsimas, Iain Dunning, Miles Lubin, D Bertsimas, I Dunning, L Lubin
- 2015

Robust optimization (RO) is a tractable method to address uncertainty in optimization problems where uncertain parameters are modeled as belonging to uncertainty sets that are commonly polyhedral or ellipsoidal. The two most frequently described methods in the literature for solving RO problems are reformulation to a deterministic optimization problem or an… (More)

It is increasingly important for researchers and practitioners to be familiar with methods and software tools for analyzing large data sets, formulating and solving large-scale mathematical optimization models, and sharing solutions using interactive media. Unfortunately, advanced software tools are seldom included in curricula of graduate-level operations… (More)