Month: June 2026

A Catalog of Formulations for the Multi-Follower Discrete Bilevel Network Design Problem

Categories Bilevel Optimization, Branch and Cut Algorithms, Network Optimization Tags , , ,

Network design problems increasingly arise in settings where strategic infrastructure decisions and operational routing choices are made by different actors. Such interactions are naturally modeled as bilevel problems: a network operator designs or modifies a network, while users respond by selecting routes according to their own utilities. This structure captures many applications in transportation and … Read more

Global convergence of a coderivative-based regularized Newton method with damping for nonsmooth optimization

Categories Nonsmooth Optimization

In this paper, we propose and analyze a globally convergent regularized Newton method with positive definite regularization for solving nonsmooth optimization problems. Our approach leverages the coderivative-generated second-order subdifferential (generalized Hessian) and replaces the identity matrix in traditional algorithms with a general positive-definite symmetric matrix to regularize the generalized Hessian. By appropriately selecting the regularization … Read more

Operation-Aware Deterministic Global Optimization of Carnot Battery Design using Hybrid Modeling

Categories Energy, Global Optimization Applications Tags , , , , ,

The global demand for grid-scale energy storage continues to increase. Carnot batteries (CBs) are not geographically constrained and consist of mature components. Furthermore, charging power, discharging power, and storage capacity can be sized independently and tailored to the intended use case. Designing an optimal CB also requires considering the resulting operational behavior. While design and … Read more

Advanced Geometrical Test for Interval Branch and Bound methods

Categories Global Optimization, Robust Optimization Tags , , , ,

The Interval Branch and Bound (IBB) method is a widely used approach for solving nonlinear programming problems, especially when a rigorous solution is required. It uses Interval Arithmetic to handle rounding errors. Although numerous variants of the IBB method have been proposed in the literature, relatively few implementations incorporate Karush-Kuhn-Tucker or Fritz-John (FJ) optimality conditions … Read more

De-risking solutions to optimization problems

Categories Bilevel Optimization, Convex and Nonsmooth Optimization, Robust Optimization Tags

We develop a cutting-plane methodology that adjusts solutions to optimization problems so as to reduce features that bring about exposure to risk, such as concentration of assets or resources. The methodology is agnostic to the representation of risk but has provably good attributes. Our procedure aims to reduce the appropriate risk metric without accruing a … Read more

Lower Bounds for Feasibility and Stationarity in First-Order Nonconvex Constrained Optimization

Categories Constrained Nonlinear Optimization, Nonlinear Optimization

We study oracle-complexity lower bounds for first-order methods applied to smooth equality-constrained nonconvex optimization, separating two components of approximate KKT accuracy: feasibility and stationarity. Under iteration-wise Jacobian regularity, we prove a lower bound of order \(\Omega(\frac{L_c\Delta_c}{\sigma^2}+\log\log(\frac{\sigma^2}{L_c\epsilon}))\) to achieve \(\epsilon\)-feasibility. For stationarity, we construct a nonlinear equality-constrained hard instance whose multiplier-minimized stationarity residual reduces exactly to … Read more

A Fletcher’s Augmented Lagrangian-Based Stochastic First-Order Method for Nonconvex Equality-Constrained Optimization

Categories Constrained Nonlinear Optimization, Nonlinear Optimization

In this paper, we study nonconvex equality-constrained optimization problems in which only stochastic first-order approximations of the objective and constraint functions are available. Owing to the stochasticity in both objective and constraints, most existing stochastic first-order methods incur relatively high oracle complexity, particularly in terms of stochastic constraint function evaluations. To address this issue, we … Read more

Constrained Variable Projection for Structured Problems

Categories Bilevel Optimization, Nonlinear Optimization, Optimization in Data Science Tags , ,

Variable projection is a classical technique for separable nonlinear least-squares problems, in which variables that enter linearly are eliminated exactly, yielding a reduced nonlinear problem. By expressing this framework as a particular instance of a broader class of bilevel optimization problems, we develop a constrained variable-projection framework for data-science models, where the remaining variables are … Read more

Skip or Insert? A Priori Optimization for the Vehicle Routing Problem with Time Windows and Stochastic Customers

Categories Combinatorial Optimization, Production and Logistics, Stochastic Programming Tags , , , , , , ,

We study an extension of the vehicle routing problem with time windows by incorporating stochastic customers, i.e., ad-hoc service requests. The uncertainty in stochastic customers is captured through scenarios. Two a priori optimization approaches, a classical and a new one lead to two different problems, both of which are modeled as scenario-based two-stage stochastic programs. … Read more