stochastic optimization – Optimization Online

Stochastic Augmented Lagrangian Framework with Second-Order Convergence Guarantees for Nonconvex Expectation-Constrained Optimization

Published: 2026/09/23

In this paper, we propose and analyze an augmented Lagrangian framework for solving stochastic nonconvex optimization problems with expectation-based equality constraints over a closed and convex constraint set. The framework generates a sequence of nonconvex primal subproblems, which are solved inexactly using stochastic second-order methods. We establish iteration complexity results for obtaining approximate second-order stationary … Read more

Two-stage approach for the predispatch problem with uncertain demand using splitting variables in interior-point methods

Published: 2026/09/16

Applications - Science and Engineering, Quadratic Programming, Stochastic Programming interior point methods, optimal power flow, Splitting Variables., stochastic optimization

The stochastic predispatch optimal power flow problem aims to minimize generation costs and transmission losses subject to network constraints under demand uncertainty. We formulate it as a two-stage stochastic quadratic optimization problem with fixed recourse, in which hydroelectric generation constitutes the here-and-now decision, while thermal generation and transmission flows are recourse decisions. Using a splitting-variable … Read more

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

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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Lipschitz Gradient Guarantees for Probability Functions and a New Algorithm for Probability Maximization

Published: 2026/05/29

Stochastic Programming probability functions, probability maximization, stochastic optimization, variational analysis

This work studies probability functions that appear in stochastic programming models. Although their differentiability has been widely investigated, the Lipschitz continuity of their gradients, crucial for the design and analysis of modern optimization algorithms, has received little attention. We develop a general framework that ensures differentiability and gradient Lipschitz continuity under practical conditions. Our framework … Read more

Stochastic block coordinate and function alternation for multi-objective optimization and learning

Published: 2026/05/14

Multi-Criteria Optimization Alternating Optimization, block coordinate descent method, multi-objective optimization, stochastic optimization

Multi-objective optimization is central to many engineering and machine learning applications, where multiple objectives must be optimized in balance. While multi-gradient based optimization methods combine these objectives in each step, such methods require computing gradients with respect to all variables at every iteration, resulting in high computational costs in large-scale settings. In this work, we … Read more

Complexity of an inexact stochastic SQP algorithm for equality constrained optimization

Published: 2026/04/15, Updated: 2026/04/29

Constrained Nonlinear Optimization, Stochastic Programming nonlinear optimization, sequential quadratic optimization, stochastic optimization, worst-case complexity

In this paper, we consider nonlinear optimization problems with a stochastic objective function and deterministic equality constraints. We propose an inexact two-stepsize stochastic sequential quadratic programming (SQP) algorithm and analyze its worst-case complexity under mild assumptions. The method utilizes a step decomposition strategy and handles stochastic gradient estimates by assigning different stepsizes to different components … Read more

Deep Learning for Sequential Decision Making under Uncertainty: Foundations, Frameworks, and Frontiers

Published: 2026/04/12

I. Esra Buyuktahtakin Toy

Data Science Algorithms, Optimization in Data Science, Stochastic Programming decision making under uncertainty, Decision-focused learning, deep learning, learning-to-optimize, Machine learning and optimization, markov decision processes, multi-stage stochastic programming, operations research, optimization under uncertainty, reinforcement learning, sequential decision making, stochastic optimization

Artificial intelligence (AI) is moving increasingly beyond prediction to support decisions in complex, uncertain, and dynamic environments. This shift creates a natural intersection with operations research and management sciences (OR/MS), which have long offered conceptual and methodological foundations for sequential decision-making under uncertainty. At the same time, recent advances in deep learning, including feedforward neural … Read more

An Inexact Trust-Region Method for Structured Nonsmooth Optimization with Application to Risk-Averse Stochastic Programming

Published: 2026/04/08

Drew P. Kouri

Nonsmooth Optimization, Optimization of Systems modeled by PDEs, Stochastic Programming adaptivity, nonsmooth optimization, risk averse optimization, saddle point problems, stochastic optimization, Trust Regions

We develop a trust-region method for efficiently minimizing the sum of a smooth function, a nonsmooth convex function, and the composition of a finite-valued support function with a smooth function. Optimization problems with this structure arise in numerous applications including risk-averse stochastic programming and subproblems for nonsmooth penalty nonlinear programming methods. Our method permits the … Read more

AI for Enhancing Operations Research of Agriculture and Energy

Published: 2025/12/29

(Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Global Optimization Agricultural Planning, energy systems, Learning-Enhanced Optimization, mixed-integer nonlinear programming, optimal power flow, reinforcement learning, stochastic optimization, unit commitment

This paper surveys optimization problems arising in agriculture, energy systems, and water-energy coordination from an operations research perspective. These problems are commonly formulated as integer nonlinear programs, mixed-integer nonlinear programs, or combinatorial set optimization models, characterized by nonlinear physical constraints, discrete decisions, and intertemporal coupling. Such structures pose significant computational challenges in large-scale and repeated-solution … Read more