Complexity of near-optimal robust versions of multilevel optimization problems

11/02/2020
by   Mathieu Besançon, et al.
0

Near-optimality robustness extends multilevel optimization with a limited deviation of a lower level from its optimal solution, anticipated by higher levels. We analyze the complexity of near-optimal robust multilevel problems, where near-optimal robustness is modelled through additional adversarial decision-makers. Near-optimal robust versions of multilevel problems are shown to remain in the same complexity class as the problem without near-optimality robustness under general conditions.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
08/12/2019

Near-optimal Robust Bilevel Optimization

Bilevel optimization studies problems where the optimal response to a se...
research
05/28/2021

A Gradient Method for Multilevel Optimization

Although application examples of multilevel optimization have already be...
research
05/28/2019

A near-optimal algorithm for approximating the John Ellipsoid

We develop a simple and efficient algorithm for approximating the John E...
research
02/16/2021

Unambiguous DNFs and Alon-Saks-Seymour

We exhibit an unambiguous k-DNF formula that requires CNF width Ω̃(k^2),...
research
11/02/2020

Sparse Multilevel Roadmaps on Fiber Bundles for High-Dimensional Motion Planning

Sparse roadmaps are important to compactly represent state spaces, to de...
research
12/24/2021

Tractable and Near-Optimal Adversarial Algorithms for Robust Estimation in Contaminated Gaussian Models

Consider the problem of simultaneous estimation of location and variance...
research
03/30/2022

Optimal Learning

This paper studies the problem of learning an unknown function f from gi...

Please sign up or login with your details

Forgot password? Click here to reset