lagrange duality – Optimization Online

On Supportedness-Promoting Image Space Transformations in Multiobjective Optimization

Published: 2025/11/26

Multi-Criteria Optimization lagrange duality, multiobjective optimization, power transformation, supportedness, Weighted sum scalarization

We study the supportedness of nondominated points of multiobjective optimization problems, that is, whether they can be obtained via weighted sum scalarization. One key question is how supported points behave under an efficiency-preserving transformation of the original problem. Under a differentiability assumption, we characterize the transformations that preserve both efficiency and supportedness as the component-wise … Read more

A guided tour through the zoo of paired optimization problems

Published: 2025/10/29

Oliver Stein

Bilevel Optimization, Game Theory, Nonlinear Optimization bicriteria optimization, bilevel problem, decomposition, lagrange duality, minimax problem, Nash equilibrium problem, robust optimization, saddle problem, semi-infinite problem, two-stage stochastic optimization

Many mathematical models base on the coupling of two or more optimization problems. This paper surveys possibilities to couple two optimization problems and discusses how solutions of the different models are interrelated with each other. The considered pairs stem from the fields of standard and generalized Nash equilibrium problems, optimistic and pessimistic bilevel problems, saddle … Read more

In pursuit of a root

Published: 2007/06/28

Michael P. Friedlander

Ewout van den Berg

Convex Optimization basis pursuit, gradient projection, lagrange duality

The basis pursuit technique is used to find a minimum one-norm solution of an underdetermined least-squares problem. Basis pursuit denoise fits the least-squares problem only approximately, and a single parameter determines a curve that traces the trade-off between the least-squares fit and the one-norm of the solution. We show that the function that describes this … Read more