On parallel solvers for stochastic optimization with recourse

Cosmin Petra (Lawrence Livermore National Laboratory)
Thursday, November 10, 2016 - 11:30

In this talk I will discuss my work towards developing parallel linear algebra libraries for stochastic optimization. I will mainly focus on presenting a Schur complement technique that decomposes the linear systems solved within interior-point methods. The solver using this approach, PIPS-IPM, proved to be scalable on 32,768 nodes on Titan at Oak Ridge, as well as on an older BG/P machine at Argonne. To bridge the space between scalability and performance, a considerable amount of work was dedicated to obtain state-of-the-art intra-node performance (measured for example by sustained FLOPS). This was achieved by developing an incomplete augmented factorization algorithm in collaboration with the PARDISO team to circumvent the well-known limitation(s) in the multi-core parallelization of triangular solves with multiple right-hand sides. I will also give an overview of a parallel implementation of the revised simplex methods (code name PIPS-S), which is also targeted at stochastic optimization. Numerical experiments on parallel computers with the two solvers will be also presented and discussed. In the second part of my talk I will provide a short overview of the existing software capabilities in stochastic optimization developed by my group over the years. These capabilities consist of PIPS suite of solvers (PIPS-IPM, PIPS-S, and the younger sibling PIPS-NLP, which is for nonlinear stochastic problems) as well as the StructJuMP modelling environment. StructJuMP is a parallel, distributed memory extension of Julia Mathematical Programming (JuMP) algebraic modeling language. StructJuMP is aimed at the fast specification and quick prototyping of large stochastic problems by domain specialists without requiring knowledge of parallel computing. To illustrate this, I will present StructJuMP models arising in the optimization of energy systems and the computational approach behind the under-the-hood parallelization.