Related papers: Globally Solving a Class of Bilevel Programs with …
This paper considers a bilevel program. To solve this bilevel program, it is generally necessary to transform it into some single-level optimization problem. One approach is to replace the lower-level program by its KKT conditions to…
The implementation of electricity markets based on locational marginal pricing in a multi-settlement process has allowed wholesale competition, with pricing mechanisms that incentivize the optimal allocation of generation, transmission, and…
The existing research on market price-affecting agents, i.e. price makers, neglects or simplifies the nature of AC power flows in the power system as it predominantly relies on DC power flows. This paper proposes a novel bilevel formulation…
In order to coordinate the scheduling problem between an isolated microgrid (IMG) and electric vehicle battery swapping stations (BSSs) in multi-stakeholder scenarios, a new bi-level optimal scheduling model is proposed for promoting the…
The fast uptake of distributed energy resources (DERs) presents increasing challenges for managing hosting capacity in distribution networks. Existing solutions include direct load control, operating envelopes, and price-based control…
Interest in bilevel optimization has grown in recent years, partially due to its applications to tackle challenging machine-learning problems. Several exciting recent works have been centered around developing efficient gradient-based…
Energy communities (ECs) are emerging as a promising decentralized model for managing cooperative distributed energy resources (DERs). As these communities expand and their operations become increasingly integrated into the grid, ensuring…
Bilevel optimization is an important class of optimization problems where one optimization problem is nested within another. While various methods have emerged to address unconstrained general bilevel optimization problems, there has been a…
Wireless networks are evolving from radio resource providers to complex systems that also involve computing, with the latter being distributed across edge and cloud facilities. Also, their optimization is shifting more and more from a…
We consider the profit-maximization problem solved by an electricity retailer who aims at designing a menu of contracts. This is an extension of the unit-demand envy-free pricing problem: customers aim to choose a contract maximizing their…
Usually, bilevel optimization problems need to be transformed into single-level ones in order to derive optimality conditions and solution algorithms. Among the available approaches, the replacement of the lower-level problem by means of…
We design and analyze a novel accelerated gradient-based algorithm for a class of bilevel optimization problems. These problems have various applications arising from machine learning and image processing, where optimal solutions of the two…
We propose a new family of multilevel methods for unconstrained minimization. The resulting strategies are multilevel extensions of high-order optimization methods based on q-order Taylor models (with q >= 1) that have been recently…
Bilevel optimization is a central tool in machine learning for high-dimensional hyperparameter tuning. Its applications are vast; for instance, in imaging it can be used for learning data-adaptive regularizers and optimizing forward…
Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…
The increasing integration of renewable energy sources and distributed energy resources (DER) into modern power systems introduces significant uncertainty, posing challenges for maintaining grid flexibility and reliability. Hybrid energy…
Bilevel optimization involves a hierarchical structure where one problem is nested within another, leading to complex interdependencies between levels. We propose a single-loop, tuning-free algorithm that guarantees anytime feasibility,…
We study a class of two-stage stochastic programs, namely, those with fixed recourse matrix and fixed costs, and linear second stage. We show that, under mild assumptions, the problem can be solved with just one scenario, which we call an…
In this paper we consider spatial networks that realize a balance between an infrastructure cost (the cost of wire needed to connect the network in space) and communication efficiency, measured by average shortest pathlength. A global…
Time-and-Level-of-Use (TLOU) is a recently proposed pricing policy for energy, extending Time-of-Use with the addition of a capacity that users can book for a given time frame, reducing their expected energy cost if they respect this…