On the existence of Lagrange multipliers in conic programming
The existence of Lagrange multipliers at a solution of a nonlinear optimization problem constitutes one of the cornerstones of modern optimization theory, with many important consequences for guiding algorithmic procedures towards a solution, defining stopping criteria, performing stability analysis, and several other aspects. However, the proof of this result is often intricate, relying on non-trivial … Read more
Scalable Finite Adaptability via Polyhedral Partition and Learning
We study finite adaptability for decision-making under uncertainty, where a small set of candidate solutions is prepared in advance and the best response is selected after uncertainty is realized. While existing methods have made significant progress on exact formulations, scalability remains a persistent challenge due to (i) the combinatorial nature of assigning decisions to uncertainty … Read more
Exact Approaches for the Maximum Mortality Rate Clique Problem
This paper develops exact solution methods for the maximum mortality rate clique problem, which aims to identify a cluster of diseases in a comorbidity graph associated with the highest mortality rate among patients whose healthcare encounters are recorded in electronic health records. We establish the NP-hardness of the problem and propose two mixed-integer linear programming … Read more
Inexactly Smooth Performance Estimation and New Optimized Gradient Methods
We consider a general class of “inexactly smooth” convex functions, providing a universal model capturing as special cases $L$-smooth, $M$-Lipschitz, and H\”older smooth functions, and any combination thereof. Such functions possess a calculus closely following that of smooth functions. Our main results provide inexactly smooth functions with interpolation theorems that are necessary and sufficient … Read more
Relief-based Anesthesiologist Scheduling with Stochastic Surgery Durations
We present a two-stage stochastic programming model for scheduling anesthesiologists to operating rooms under uncertainty in surgery durations. The proposed model takes a relief order to balance anesthesiologists’ workload as input and captures the trade-offs between anesthesiologist relief times, handoffs and under-staffing. To address the computational challenges of solving the proposed model, we derive supervalid … Read more
Covering for Set-Valued Mappings in the Absence of Metric Regularity
Covering properties build the foundation of stability and sensitivity analysis of solutions to a generalized equation and more specific optimization-related stationarity and equilibrium problems. It has been well-understood that metric regularity of the mapping defining the generalized equation is a key to furnish Lipschitzian stability of the solution of interest. With this work, we want … Read more
Extrapolation-based Direct Search for Nonsmooth Stochastic Zeroth-Order Optimization
We propose and analyze a stochastic direct-search method for unconstrained zeroth-order minimization of locally Lipschitz, possibly nonsmooth, objectives. The method combines random polling directions with a stochastic extrapolating line search based on a sufficient-decrease test of order \(p\). Under conditional accuracy assumptions on the stochastic estimates, which can be verified for mean-zero finite-higher-moment oracle noise … Read more
Stochastic Bilevel Optimization for the Network Design of Multimodal Transit Systems with Heterogeneous Rider Preferences under Uncertain Travel Times and Demand
Designing efficient and user-friendly multimodal transit networks is critical for modern urban mobility. We study a novel stochastic multimodal transit network design problem that integrates fixed-route services with on-demand shuttles, explicitly accounting for heterogeneous rider preferences, uncertain travel times, and passenger demand. The hierarchical decision-making process is modeled using a two-stage stochastic bilevel optimization problem, … Read more
Nested Benders Decomposition for Large-Scale Multi-Follower Bilevel Optimization
We propose a scalable nested Benders decomposition (BD) framework for single-leader, multi-follower bilevel optimization problems. The proposed framework is applicable to bilevel optimization problems in which each follower solves a linear program and is particularly well suited for instances involving a large number of followers. By identifying the upper-level decisions as complicating variables, the method … Read more