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Bilevel optimization has found successful applications in various machine learning problems, including hyper-parameter optimization, data cleaning, and meta-learning. However, its huge computational cost presents a significant challenge for…

Machine Learning · Computer Science 2024-11-05 Xiaoyu Wang , Rui Pan , Renjie Pi , Jipeng Zhang

Bilevel optimization formulates hierarchical decision-making processes that arise in many real-world applications such as in pricing, network design, and infrastructure defense planning. In this paper, we consider a class of bilevel…

Optimization and Control · Mathematics 2021-04-20 Geunyeong Byeon , Pascal Van Hentenryck

Bilevel optimization, a hierarchical mathematical framework where one optimization problem is nested within another, has emerged as a powerful tool for modeling complex decision-making processes in various fields such as economics,…

Machine Learning · Computer Science 2024-12-25 Omer Ekmekcioglu , Nursen Aydin , Juergen Branke

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

Optimization and Control · Mathematics 2023-04-25 Ruichen Jiang , Nazanin Abolfazli , Aryan Mokhtari , Erfan Yazdandoost Hamedani

In this paper, we consider a bilevel polynomial optimization problem where the objective and the constraint functions of both the upper and the lower level problems are polynomials. We present methods for finding its global minimizers and…

Optimization and Control · Mathematics 2016-01-14 V. Jeyakumar , J. B. Lasserre , G. Li , T. S. Pham

In electricity markets, customers are increasingly constrained by their budgets. A budget constraint for a user is an upper bound on the price multiplied by the quantity. However, since prices are determined by the market equilibrium, the…

Computer Science and Game Theory · Computer Science 2026-03-24 Lila Perkins , Baosen Zhang

The growing integration of renewable energy sources necessitates adequate reserve capacity to maintain power balance. However, in market clearing, power companies with flexible resources may submit strategic bids to maximize profits,…

Systems and Control · Electrical Eng. & Systems 2025-06-26 Yun Xu , Yunxiao Bai , Yunyong Zhang , Peng Wang , Xuelin Wang , Jiqun Guo , Kaijun Xie , Rusheng Zhao

This paper studies the joint optimization of edge node activation and resource pricing in edge computing, where an edge computing platform provides heterogeneous resources to accommodate multiple services with diverse preferences. We cast…

Optimization and Control · Mathematics 2025-07-15 Duong Thuy Anh Nguyen , Tarannum Nisha , Ni Trieu , Duong Tung Nguyen

We consider class of equilibrium models including the implicit Walras supply-demand and competitive models. Such a model in this class, in general, is ill-posed. We formulate such a model in the form a variational inequality having certain…

Optimization and Control · Mathematics 2024-12-25 Nguyen Ngoc Hai , Le Dung Muu , Nguyen Van Quy

We consider a smooth pessimistic bilevel optimization problem, where the lower-level problem is convex and satisfies the Slater constraint qualification. These assumptions ensure that the Karush-Kuhn-Tucker (KKT) reformulation of our…

Optimization and Control · Mathematics 2025-09-15 Imane Benchouk , Lateef Jolaoso , Khadra Nachi , Alain Zemkoho

In response to the increasing complexity of electricity markets due to low-carbon requirements and the integration of sustainable energy sources, this paper proposes a dynamic quantum computing enhanced bilevel optimization model for…

Systems and Control · Electrical Eng. & Systems 2024-10-29 Shuyang Zhu , Ziqing Zhu

When the lower-level optimal solution set-valued mapping of a bilevel optimization problem is not single-valued, we are faced with an ill-posed problem, which gives rise to the optimistic and pessimistic bilevel optimization problems, as…

Optimization and Control · Mathematics 2024-08-13 Imane Benchouk , Khadra Nachi , Alain Zemkoho

In recent years, significant efforts for improving the technical and the economic performance of smart grids have been applied with the presence of different players making decisions in these grids. This paper proposes a bi-level…

Optimization and Control · Mathematics 2020-09-30 Jaber Valinejad , Mousa Marzband , Mert Korkali , Yijun Xu , Ameena Saad Al Sumaiti

Electricity market operators worldwide use mixed-integer linear programming to solve the allocation problem in wholesale electricity markets. Prices are typically determined based on the duals of relaxed versions of this optimization…

Computer Science and Game Theory · Computer Science 2023-12-13 Mete Şeref Ahunbay , Martin Bichler , Teodora Dobos , Johannes Knörr

Bilevel optimization has gained prominence in various applications. In this study, we introduce a framework for solving bilevel optimization problems, where the variables in both the lower and upper levels are constrained on Riemannian…

Optimization and Control · Mathematics 2024-11-05 Andi Han , Bamdev Mishra , Pratik Jawanpuria , Akiko Takeda

Demand response (DR) leverages demand-side flexibility, offering a promising approach to enhance market conditions like mitigating wholesale price spikes. However, poorly chosen DR locations can inadvertently increase electricity prices.…

Systems and Control · Electrical Eng. & Systems 2024-08-06 Yufan Zhang , Honglin Wen , Tao Feng , Yize Chen

Solutions of bilevel optimization problems tend to suffer from instability under changes to problem data. In the optimistic setting, we construct a lifted formulation that exhibits desirable stability properties under mild assumptions that…

Optimization and Control · Mathematics 2025-02-25 Johannes O. Royset

A bilevel program is an optimization problem whose constraints involve another optimization problem. This paper studies bilevel polynomial programs (BPPs), i.e., all the functions are polynomials. We reformulate BPPs equivalently as…

Optimization and Control · Mathematics 2016-11-04 Jiawang Nie , Li Wang , Jane Ye

In this paper we consider a distributed optimization scenario in which a set of agents has to solve a convex optimization problem with separable cost function, local constraint sets and a coupling inequality constraint. We propose a novel…

Systems and Control · Computer Science 2018-04-25 Ivano Notarnicola , Giuseppe Notarstefano

In this paper, we consider bilevel optimization problem where the lower-level has coupled constraints, i.e. the constraints depend both on the upper- and lower-level variables. In particular, we consider two settings for the lower-level…

Optimization and Control · Mathematics 2025-03-14 Xiaotian Jiang , Jiaxiang Li , Mingyi Hong , Shuzhong Zhang