Related papers: Randomized Progressive Hedging methods for Multi-s…
We investigate multi-stage demand uncertainty for the multi-item multi-echelon capacitated lot sizing problem with setup carry-over. Considering a multi-stage decision framework helps to quantify the benefits of being able to adapt…
The progressive hedging algorithm (PHA) is a cornerstone among algorithms for large-scale stochastic programming problems. However, its traditional implementation is hindered by some limitations, including the requirement to solve all…
This paper describes the application of a Progressive Hedging (PH) algorithm to the least-cost var planning under uncertainty. The method PH is a scenario-based decomposition technique for solving stochastic programs, i.e., it decomposes a…
Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…
This article aims to explain the Nested Benders algorithm for the solution of large-scale stochastic programming problems in a way that is intelligible to someone coming to it for the first time. In doing so it gives an explanation of…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
We address the stochastic transmission expansion planning (STEP) problem under uncertainty in renewable generation capacity and demand. STEP's objective is to minimize total transmission investment and generation costs. To tackle the…
Stochastic control with both inherent random system noise and lack of knowledge on system parameters constitutes the core and fundamental topic in reinforcement learning (RL), especially under non-episodic situations where online learning…
We propose a framework, called neural-progressive hedging (NP), that leverages stochastic programming during the online phase of executing a reinforcement learning (RL) policy. The goal is to ensure feasibility with respect to constraints…
Stochastic Optimization is a cornerstone of operations research, providing a framework to solve optimization problems under uncertainty. Despite the development of numerous algorithms to tackle these problems, several persistent challenges…
Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little…
Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level…
We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…
We introduce the class of multistage stochastic optimization problems with a random number of stages. For such problems, we show how to write dynamic programming equations and detail the Stochastic Dual Dynamic Programming algorithm to…
Multistage stochastic programming is a powerful tool allowing decision-makers to revise their decisions at each stage based on the realized uncertainty. However, in practice, organizations are not able to be fully flexible, as decisions…
In this work, we study a novel class of projection-based algorithms for linearly constrained problems (LCPs) which have a lot of applications in statistics, optimization, and machine learning. Conventional primal gradient-based methods for…
We study optimization algorithms for the finite sum problems frequently arising in machine learning applications. First, we propose novel variants of stochastic gradient descent with a variance reduction property that enables linear…
This paper begins with a study on the dual representations of risk and regret measures and their impact on modeling multistage decision making under uncertainty. A relationship between risk envelopes and regret envelopes is established by…
Randomized rounding is a technique that was originally used to approximate hard offline discrete optimization problems from a mathematical programming relaxation. Since then it has also been used to approximately solve sequential stochastic…
Multilevel optimization has gained renewed interest in machine learning due to its promise in applications such as hyperparameter tuning and continual learning. However, existing methods struggle with the inherent difficulty of efficiently…