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Related papers: On Stability in Optimistic Bilevel Optimization

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In this paper we study convex bi-level optimization problems for which the inner level consists of minimization of the sum of smooth and nonsmooth functions. The outer level aims at minimizing a smooth and strongly convex function over the…

Optimization and Control · Mathematics 2017-02-15 Shoham Sabach , Shimrit Shtern

In this paper, we study a class of stochastic bilevel optimization problems, also known as stochastic simple bilevel optimization, where we minimize a smooth stochastic objective function over the optimal solution set of another stochastic…

Optimization and Control · Mathematics 2023-08-16 Jincheng Cao , Ruichen Jiang , Nazanin Abolfazli , Erfan Yazdandoost Hamedani , Aryan Mokhtari

This paper firstly proposes a convex bilevel optimization paradigm to formulate and optimize popular learning and vision problems in real-world scenarios. Different from conventional approaches, which directly design their iteration schemes…

Computer Vision and Pattern Recognition · Computer Science 2021-12-30 Risheng Liu , Long Ma , Xiaoming Yuan , Shangzhi Zeng , Jin Zhang

Inverse problems are key issues in several scientific areas, including signal processing and medical imaging. Data-driven approaches for inverse problems aim for learning model and regularization parameters from observed data samples, and…

Optimization and Control · Mathematics 2024-11-28 Mathias Staudigl , Simon Weissmann , Tristan van Leeuwen

Bilevel linear programs (BLPs) form a class of hierarchical decision-making problems in which both the upper-level and the lower-level decision-makers, known as the leader and the follower, respectively, solve linear optimization problems.…

Computational Complexity · Computer Science 2025-11-20 Sergey S. Ketkov , Oleg A. Prokopyev

Although application examples of multilevel optimization have already been discussed since the 1990s, the development of solution methods was almost limited to bilevel cases due to the difficulty of the problem. In recent years, in machine…

Optimization and Control · Mathematics 2021-10-27 Ryo Sato , Mirai Tanaka , Akiko Takeda

Stochastic bilevel optimization generalizes the classic stochastic optimization from the minimization of a single objective to the minimization of an objective function that depends the solution of another optimization problem. Recently,…

Optimization and Control · Mathematics 2022-04-01 Tianyi Chen , Yuejiao Sun , Quan Xiao , Wotao Yin

In this paper, we introduce a bilevel optimization framework for addressing inverse mean-field games, alongside an exploration of numerical methods tailored for this bilevel problem. The primary benefit of our bilevel formulation lies in…

Optimization and Control · Mathematics 2024-11-13 Jiajia Yu , Quan Xiao , Tianyi Chen , Rongjie Lai

Bilevel programs are optimization problems where some variables are solutions to optimization problems themselves, and they arise in a variety of control applications, including: control of vehicle traffic networks, inverse reinforcement…

Optimization and Control · Mathematics 2017-09-27 Aurélien Ouattara , Anil Aswani

Here, necessary optimal condition for Optimistic Bilevel programming problem is obtained in Asplund spaces. Also we have got necessary optimal conditions in finite dimensional spaces, by assuming differentiability on the given functions.

Optimization and Control · Mathematics 2019-01-11 Suvendu Pattanaik

Bilevel optimization provides a powerful framework for modelling hierarchical decision-making systems. This work presents a sensitivity-based algorithm that addresses the bilevel structure directly by treating the lower-level optimal…

Optimization and Control · Mathematics 2026-05-28 Eduardo Nolasco , Ross D. King , Vassilios S. Vassiliadis

Stochastic bilevel optimization tackles challenges involving nested optimization structures. Its fast-growing scale nowadays necessitates efficient distributed algorithms. In conventional distributed bilevel methods, each worker must…

Optimization and Control · Mathematics 2024-05-30 Yutong He , Jie Hu , Xinmeng Huang , Songtao Lu , Bin Wang , Kun Yuan

Inverse linear programming (LP) has received increasing attention due to its potential to generate efficient optimization formulations that can closely replicate the behavior of a complex system. However, inversely inferred parameters and…

Optimization and Control · Mathematics 2022-02-22 Zahed Shahmoradi , Taewoo Lee

We study a class of algorithms for solving bilevel optimization problems in both stochastic and deterministic settings when the inner-level objective is strongly convex. Specifically, we consider algorithms based on inexact implicit…

Optimization and Control · Mathematics 2022-07-12 Michael Arbel , Julien Mairal

This work uniquely combines an affine linear decision rule known from adjustable robustness with min-max-regret robustness. By doing so, the advantages of both concepts can be obtained with an adjustable solution that is not…

Optimization and Control · Mathematics 2024-12-02 Kerstin Schneider , Helene Krieg , Dimitri Nowak , Karl-Heinz Küfer

This paper proposes a bilevel hierarchy of strengthened complex moment relaxations for complex polynomial optimization. The key trick entails considering a class of positive semidefinite conditions that arise naturally in characterizing the…

Optimization and Control · Mathematics 2025-05-12 Jie Wang

This paper proposes a new algorithm -- the \underline{S}ingle-timescale Do\underline{u}ble-momentum \underline{St}ochastic \underline{A}pprox\underline{i}matio\underline{n} (SUSTAIN) -- for tackling stochastic unconstrained bilevel…

Optimization and Control · Mathematics 2021-06-16 Prashant Khanduri , Siliang Zeng , Mingyi Hong , Hoi-To Wai , Zhaoran Wang , Zhuoran Yang

We develop a framework to give upper bounds on the "practical" computational complexity of stability problems for a wide range of nonlinear continuous and hybrid systems. To do so, we describe stability properties of dynamical systems using…

Systems and Control · Computer Science 2014-06-05 Sicun Gao , Soonho Kong , Edmund Clarke

Algorithms of control of differential equations solutions are under investigation in the article. Idealized and real modifications of the algorithms are distinguished. An equation, which can be the base equation for investigation of the…

Numerical Analysis · Computer Science 2016-01-05 Yu. V. Troshchiev

Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…

Optimization and Control · Mathematics 2017-12-27 Anil Aswani , Zuo-Jun Max Shen , Auyon Siddiq