Batch Learning in Stochastic Dual Dynamic Programming

We consider the stochastic dual dynamic programming (SDDP) algorithm, which is a widely employed algorithm applied to multistage stochastic programming, and propose a variant using batch learning, a technique used with success in the reinforcement learning framework. We cast SDDP as a type of Q-learning algorithm and describe its application in both risk neutral and … Read more

Improving Column-Generation for Vehicle Routing Problems via Random Coloring and Parallelization

We consider a variant of the Vehicle Routing Problem (VRP) where each customer has a unit demand and the goal is to minimize the total cost of routing a fleet of capacitated vehicles from one or multiple depots to visit all customers. We propose two parallel algorithms to efficiently solve the column-generation based linear-programming relaxation … Read more

A Parallel Hub-and-Spoke System for Large-Scale Scenario-Based Optimization Under Uncertainty

Efficient solution of stochastic programming problems generally requires the use of parallel computing resources. Here, we describe the open source package mpi-sppy, in which efficient and scalable parallelization is a central feature. We describe the overall architecture and provide computational examples and results showing scalability to the largest instances that we know of for the … Read more

A parallel splitting ALM-based algorithm for separable convex programming

The augmented Lagrangian method (ALM) provides a benchmark for tackling the canonical convex minimization problem with linear constraints. We consider a special case where the objective function is the sum of $m$ individual subfunctions without coupled variables. The recent study reveals that the direct extension of ALM for separable convex programming problems is not necessarily … Read more

On Electricity Market Equilibria with Storage: Modeling, Uniqueness, and a Distributed ADMM

We consider spot-market trading of electricity including storage operators as additional agents besides producers and consumers. Storages allow for shifting produced electricity from one time period to a later one. Due to this, multiple market equilibria may occur even if classical uniqueness assumptions for the case without storages are satisfied. For models containing storage operators, … Read more

Decomposition Methods for Solving Two-Stage Distributionally Robust Optimization Problems

Decomposition methods have been well studied for solving two-stage and multi-stage stochastic programming problems, see [29, 32, 33]. In this paper, we propose an algorithmic framework based on the fundamental ideas of the methods for solving two-stage minimax distributionally robust optimization (DRO) problems where the underlying random variables take a finite number of distinct values. … Read more

Parallel and Distributed Successive Convex Approximation Methods for Big-Data Optimization

Recent years have witnessed a surge of interest in parallel and distributed optimization methods for large-scale systems. In particular, nonconvex large-scale optimization problems have found a wide range of applications in several engineering fields. The design and the analysis of such complex, large-scale, systems pose several challenges and call for the development of new optimization … Read more

On the use of the saddle formulation in weakly-constrained 4D-VAR data assimilation

This paper discusses the practical use of the saddle variational formulation for the weakly-constrained 4D-VAR method in data assimilation. It is shown that the method, in its original form, may produce erratic results or diverge because of the inherent lack of monotonicity of the produced objective function values. Convergent, variationaly coherent variants of the algorithm … Read more

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

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

Positive-Indefinite Proximal Augmented Lagrangian Method and its Application to Full Jacobian Splitting for Multi-block Separable Convex Minimization Problems

The augmented Lagrangian method (ALM) is fundamental for solving convex programming problems with linear constraints. The proximal version of ALM, which regularizes ALM’s subproblem over the primal variable at each iteration by an additional positive-definite quadratic proximal term, has been well studied in the literature. In this paper, we show that it is not necessary … Read more