In this paper, we extend a recently proposed scenario decomposition algorithm (Ahmed (2013)) for risk-neutral 0-1 stochastic programs to the risk-averse setting. Specifically, we consider risk-averse 0-1 stochastic programs with objective functions based on coherent risk measures. Using a dual representation of a coherent risk measure, we first derive an equivalent minimax reformulation of the … Read more
Stochastic mixed-integer programs (SMIPs) deal with optimization under uncertainty at many levels of the decision-making process. When solved as extensive formulation mixed- integer programs, problem instances can exceed available memory on a single workstation. To overcome this limitation, we present PIPS-SBB: a distributed-memory parallel stochastic MIP solver that takes advantage of parallelism at multiple levels … Read more
Traditional decomposition based branch-and-bound algorithms, like branch-and-price, can be very efficient if the duality gap is not too large. However, if this is not the case, the branch-and-bound tree may grow rapidly, preventing the method to find a good solution. In this paper, we present a new decompositon algorithm, called ADGO (Alternating Direction Global Optimization … Read more
A recently proposed scenario decomposition algorithm for stochastic 0-1 programs finds an optimal solution by evaluating and removing individual solutions that are discovered by solving scenario subproblems. In this work, we develop an asynchronous, distributed implementation of the algorithm which has computational advantages over existing synchronous implementations of the algorithm. Improvements to both the synchronous … Read more
This paper presents an approach to non-stationary policy search for finite-horizon, discrete-time Markovian decision problems with large state spaces, constrained action sets, and a risk-sensitive optimality criterion. The methodology relies on modeling time variant policy parameters by a non-parametric response surface model for an indirect parametrized policy motivated by the Bellman equation. Through the interpolating … Read more
We discuss structured nonlinear programming problems arising in control applications, and we review software and hardware capabilities that enable the efficient exploitation of such structures. We focus on linear algebra parallelization strategies and discuss how these interact and influence high-level algorithmic design elements required to enforce global convergence and deal with negative curvature in a … Read more
We develop algorithmic innovations for the dual decomposition method to address two-stage stochastic programs with mixed-integer recourse and provide a parallel software implementation that we call DSP. Our innovations include the derivation of valid inequalities that tighten Lagrangian subproblems and that allow the guaranteed recovery of feasible solutions for problems without (relative) complete recourse. We … Read more
We propose ARock, an asynchronous parallel algorithmic framework for finding a fixed point to a nonexpansive operator. In the framework, a set of agents (machines, processors, or cores) update a sequence of randomly selected coordinates of the unknown variable in an asynchronous parallel fashion. As special cases of ARock, novel algorithms for linear systems, convex … Read more
This paper introduces the design and implementation of two parallel dual simplex solvers for general large scale sparse linear programming problems. One approach, called PAMI, extends a relatively unknown pivoting strategy called suboptimization and exploits parallelism across multiple iterations. The other, called SIP, exploits purely single iteration parallelism by overlapping computational components when possible. Computational … Read more
We describe the design of a C++ vector-manipulation substrate that allows first-order optimization algorithms to be expressed in a concise and readable manner, yet still achieve high performance in parallel computing environments. We use standard object-oriented techniques of encapsulation and operator overloading, combined with a novel “symbolic temporaries” delayed-evaluation system that greatly reduces the overhead … Read more