finite termination – 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

Properties of the delayed weighted gradient method

Published: 2020/03/02

Unconstrained Optimization conjugate-gradient methods, finite termination, gradient methods, krylov subspace methods, smoothing techniques

The delayed weighted gradient method, recently introduced in [13], is a low-cost gradient-type method that exhibits a surprisingly and perhaps unexpected fast convergence behavior that competes favorably with the well-known conjugate gradient method for the minimization of convex quadratic functions. In this work, we establish several orthogonality properties that add understanding to the practical behavior … Read more

Orthogonal projection algorithm for projecting onto a fnitely generated cone

Published: 2020/02/23

Convex Optimization finite termination, finitely generated cone, orthogonal projection

In this paper, an algorithm is proposed to find the nearest point of a convex cone to a given vector, which is composed of a series of orthogonal projections. Some properties of this algorithm, including the reasonability of implementation, the global convergence property and the finite termination, etc., are obtained. The proposed algorithm is more … Read more