Stochastic Programming – Optimization Online

An Adaptive Augmented Lagrangian Method for Deterministic and Stochastic Nonconvex Optimization

Published: 2026/08/27

Constrained Nonlinear Optimization, Stochastic Programming augmented Lagrangian, nonlinear optimization, stochastic optimization, worst-case complexity

We present an inexact Augmented Lagrangian algorithm for solving nonlinear, non-convex optimization problems. Unlike most recently proposed Augmented Lagrangian methods with worst-case complexity guarantees, we utilize adaptive penalty parameter updates and full dual stepsizes. We show that the method matches the best known worst-case complexity results for Augmented Lagrangian methods (up to logarithmic factors) when … Read more

The Value of Human Expertise

Published: 2026/08/23

Bradley Sturt

Robust Optimization, Stochastic Programming

We consider optimization applications with unknown parameters where the decision maker believes that the optimal value of the nominal problem—the optimization problem they would have solved if the true parameters were known—is unlikely to be large. This belief derives from information that humans have that is not captured in datasets, obtained from domain knowledge and … Read more

A Shrinkage Path Heuristic for Wasserstein Distributionally Robust Optimization

Published: 2026/08/14

Robust Optimization, Stochastic Programming distributionally robust optimization, robust optimization, sample average approximation, wasserstein ambiguity

Wasserstein distributionally robust optimization (DRO) is a versatile and widely adopted framework for decision-making under uncertainty, yet its standard deterministic reformulations generally contain non-convex inner subproblems that are challenging to solve. To address this issue, we propose a shrinkage path heuristic that reduces the solution of a DRO problem to a one-dimensional search over the … Read more

Benders Decomposition with Partial Non-Anticipativity Relaxation for Multi-Stage Stochastic Clean Energy Transition Planning

Published: 2026/08/14

Stochastic Programming benders decomposition, clean energy transition, multi-stage stochastic programming, Non-anticipativity relaxation, or in energy

We study clean energy transition planning for campus-scale integrated electricity-heat systems under both strategic level and operational level uncertainties. We formulate a multi-stage stochastic mixed-integer program that jointly optimizes investment and operational decisions for renewable generation, storage, and heat-transfer technologies whose costs and efficiencies evolve stochastically across stages. To account for short-term operational uncertainty, we … Read more

Stochastic Heterogeneous Fleet Scheduling for Airport Ground Transportation under Passenger Spillover and Service Constraints

Published: 2026/08/10

(Mixed) Integer Linear Programming, Airline Optimization, Applications - OR and Management Sciences, Facility Planning and Design, Stochastic Programming airport management, Mobility, public transportation networks, stochastic optimization

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SDDmiP.jl: A Software Package with a Provably Convergent Benders Algorithm for Multi-Stage Stochastic Mixed-Integer Programming

Published: 2026/08/06

Optimization Software and Modeling Systems, Stochastic Programming algorithms and software, Augmented Lagrangian duality, augmented lagrangian method, Bender's decomposition method, mixed-integer programming, stochastic dual dynamic programming, stochastic programming

We present an open-source software package that implements a provably convergent Benders-type decomposition algorithm for multistage stochastic integer programs. In addition to standard cut families, such as Benders, strengthened Benders, and Lagrangian cuts, the algorithm incorporates rectified linear unit (ReLU) cuts, which provide convergence guarantees for general mixed-integer state variables. However, the dual problems used … Read more

A proximal subgradient method for nonconvex stochastic optimization under the Kurdyka-Łojasiewicz condition

Published: 2026/08/05

Nonlinear Optimization, Nonsmooth Optimization, Stochastic Programming convergence rates, Kurdyka-Lojasiewicz, nonconvex optimization, proximal subgradient, stochastic approximation methods, stochastic programming

This work introduces a proximal stochastic subgradient method for minimizing the sum of an expected cost, whose integrand is potentially nonsmooth and nonconvex, and a lower semicontinuous, prox-bounded function. We target a broad class of integrands obeying a nonsmooth, localized variant of the descent lemma in the decision variable, a structural assumption that simultaneously covers … Read more

Beyond Isolated Operating Rooms: Risk-Aware Surgical Episode Scheduling in Single-Entry Networks

Published: 2026/08/05

Applications - OR and Management Sciences, Scheduling, Stochastic Programming Healthcare operations management, Operating room scheduling, risk measures, Single-entry networks, stochastic mixed-integer programming

Long wait times for elective surgery are a persistent challenge in publicly funded health systems, where hospitals must coordinate limited capacity before, during, and after the operation under considerable uncertainty. We study how a network of collaborating hospitals, such as the University Health Network in the City of Toronto, can centralize intake and jointly schedule … Read more

Robust Chance-Constrained Optimization using a Continuous Parameter Space Wasserstein-2 Ambiguity Set of Gaussian Mixtures

Published: 2026/07/18

Shibshankar Dey

Nonlinear Optimization, Robust Optimization, Stochastic Programming chance constraint, Gaussian mixture model (GMM), optimal transport, out-of-sample performance, wasserstein distance

We study distributionally robust linear chance-constrained problems in which uncertainty is modeled by a Gaussian mixture model (GMM). Finite-support distributionally robust (FDR) formulations, widely used in data-driven robust optimization, robustify over empirical mixture support points and therefore primarily stress-test the fitted nominal mixture. This can be insufficient when service reliability depends on structural misspecification of … Read more

Model-Uncertainty-Aware Residuals-Based Sample Average Approximation

Published: 2026/07/13

Robust Optimization, Stochastic Programming contextual stochastic optimization, distributionally robust optimization, Model uncertainty, stability analysis

We consider a contextual stochastic optimization (CSO) problem, where one has observations of the uncertain parameters together with concurrent observations of covariates, and the goal is to choose decisions that minimize expected cost conditioned on new covariate observations. The empirical residuals-based sample average approximation (ER-SAA) of the CSO problem constructs scenarios of uncertainty by combining … Read more