Set-valued analysis – Optimization Online

On the Convergence of Column-and-Constraint Generation Algorithms in Two-Stage Robust Optimization

Published: 2026/09/30

Henri Lefebvre

Robust Optimization column-and-constraint generation, convergence analysis, finite termination, min-max-min, Robust bilevel optimization, Set-valued analysis, two-stage robust optimization, Wait-and-see follower

We study the well-posedness and convergence of column-and-constraint generation algorithms for general two-stage robust optimization problems. The analysis is formulated in terms of regularity properties of the objective, the second-stage feasible region mapping, and the separation value function, without relying on a particular algebraic representation of the second-stage problem. We give sufficient conditions for the … Read more

Functions associated with the nonconvex second-order cone

Published: 2023/09/29, Updated: 2024/07/03

Baha Alzalg

Complementarity and Variational Inequalities, Cone Programming, Second-Order Cone Programming Nonconvex cones, second-order cone, Set-valued analysis, Set-valued function

The nonconvex second-order cone (nonconvex SOC for short) is a nonconvex extension to the convex second-order cone, in the sense that it consists of any vector divided into two sub-vectors for which the Euclidean norm of the first sub-vector is at least as large as the Euclidean norm of the second sub-vector. This cone can … Read more