Integrated Learning and Robust Optimization

Many operational decisions require solving a linear program whose cost vector is unknown at decision time and must be predicted from contextual information. Because prediction and decision are only weakly aligned, the emerging integrated learning and optimization (ILO) paradigm trains the predictor through the downstream problem, judging a prediction by the decision it induces. However, … Read more

A Domain-Specific Harness for End-to-End Automation of Optimization Research

We present AutoOPT, a domain-specific harness for end-to-end automation of optimization research. AutoOPT organizes the discovery of optimal first-order methods into four stages: numerical design through the BnB-PEP methodology; symbolic discovery of the analytic description and a convergence proof through frontier large language models (LLMs); formal verification in the Lean 4 proof assistant; and human … Read more

Attainability of properly efficient points via weighted norm scalarization

We show that efficient points can be obtained with the weighted norm scalarization under assumptions less restrictive than in the existing literature. For properly efficient points with a given trade-off bound, we provide an easy-to-compute lower bound on the norm parameter that allows the approximation of the desired points within a specified tolerance. We apply … Read more

A Momentum Trust-Region Algorithm for Unconstrained Optimization

We introduce a Momentum Trust-Region Algorithm for unconstrained optimization that incorporates Nesterov-type acceleration into the classical trust-region framework. The method builds trust-region models around a momentum-shifted point and uses an Armijo-type backtracking procedure to safeguard progress along the resulting displacement. This design preserves the robustness of trust-region methods while exploiting momentum to improve practical efficiency. … Read more

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

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

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

Optimal Nonergodic Primal-Dual Complexity of Efficient Inexact Parameter-Free Augmented Lagrangian Methods

Augmented Lagrangian (AL) methods are a classical framework for constrained optimization, but for directly verifiable approximate KKT points, known first-order complexity bounds for standard inexact AL methods are suboptimal, while the best known proximal augmented Lagrangian (PAL) bounds retain an additional logarithmic factor. We consider linearly constrained convex composite problems with a smooth convex term … Read more

Generalizing single-level relaxations for bilevel linear programs

We consider a broad class of bilevel linear programs in which the follower’s decisions are all continuous, while the leader’s decisions may include integrality restrictions. Solving such problems to optimality is known to be NP-hard. A classical approach in bilevel optimization for constructing lower and upper bounds is based on a single-level relaxation, in which … Read more