arXiv Machine Learning
Aug 19

On Stability in Optimistic Bilevel Optimization

The paper addresses instability in bilevel optimization solutions when problem data changes. It proposes a lifted formulation for the optimistic setting that remains stable under mild assumptions, without requiring convexity or smoothness. The approach accommodates integer restrictions and disjunctive constraints, relies on pointwise and local calmness of the lower-level problem, and offers computational advantages including an outer approximation algorithm.

By Johannes O. Royset
arXiv AI
Sep 10

Mathematical Programming in Machine Learning and Artificial Intelligence: A Unified Taxonomy of Models and Applications

The paper presents a unified taxonomy that classifies machine‑learning and artificial‑intelligence applications according to mathematical programming paradigms such as linear, quadratic, mixed‑integer, conic, bilevel, and others. It standardizes notation, identifies key inputs, decision variables, and principal formulations for each application, and discusses structural properties, solution strategies, and limitations. The authors compare tractability, relaxation quality, decomposition, approximation guarantees, and scalability across paradigms, emphasizing that mathematical programming serves as a disciplined interface between predictions and constrained decisions rather than a universal modeling claim.

By Chaosheng Dong
arXiv Machine Learning
Sep 15

Generation of Custom Solvers in Rust for Convex Optimization

The paper presents cvxgenrust, an open‑source tool that generates custom Rust code for solving families of parameterized convex optimization problems defined in CVXPY. It canonicalizes problem families, extracts affine maps to Clarabel cone‑program data, and produces a specialized Rust crate that updates parameters and calls Clarabel natively at runtime. The generated solver can also be exposed to Python and registered as a custom CVXPY solver, supporting a wide range of convex problems up to semidefinite and exponential‑cone programs, and demonstrates reduced runtime compared to direct CVXPY solves and performance comparable to CVXPYgen.

By Hao Zhu, Joschka Boedecker