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Deterministic sample average approximations of stochastic programming problems with recourse are suitable for a scenario-based parallelization. In this paper the parallelization is obtained by using an interior-point method and a Schur complement mechanism for the interior-point linear systems. However, the direct linear solves involving the dense Schur… (More)

The present work aims at comparing the performance of several quadratic programming (QP) solvers for simulating large-scale frictional rigid-body systems. Traditional time-stepping schemes for simulation of multibody systems are formulated as linear complementarity problems (LCPs) with copositive matrices. Such LCPs are generally solved by means of… (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)

A higher order corrector-predictor interior-point method is proposed for solving sufficient linear complementarity problems. The algorithm produces a sequence of iterates in the N − ∞ neighborhood of the central path. The algorithm does not depend on the handicap κ of the problem. It has O((1 + κ) √ nL) iteration complexity and is superlinearly convergent… (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)

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)

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)

In this article we construct and analyze multigrid preconditioners for discretizations of operators of the form D λ + K * K, where D λ is the multiplication with a relatively smooth function λ > 0 and K is a compact linear operator. These systems arise when applying interior point methods to the minimization problem minu 1 2 (||Ku − f || 2 + β||u|| 2) with… (More)