Related papers: Globally Solving a Class of Bilevel Programs with …
Distributed renewable resources owned by prosumers can be an effective way of fortifying grid resilience and enhancing sustainability. However, prosumers serve their own interests and their objectives are unlikely to align with that of…
In this work, we propose derivative-free framework for bilevel optimization. We consider both the upper and lower-level problems with bound constraints on the variables, as well as general nonlinear constraints, assuming that first-order…
We consider the standard optimistic bilevel optimization problem, in particular upper- and lower-level constraints can be coupled. By means of the lower-level value function, the problem is transformed into a single-level optimization…
Bilevel optimization (BLO) problem, where two optimization problems (referred to as upper- and lower-level problems) are coupled hierarchically, has wide applications in areas such as machine learning and operations research. Recently, many…
In this paper, we propose a bilateral peer-to-peer (P2P) energy trading scheme under single-contract and multi-contract market setups, both as an assignment game, and a special class of coalitional games. {The proposed market formulation…
This paper aims to solve a class of CEC benchmark constrained optimization problems that have been widely studied by nature-inspired optimization algorithms. Global optimality condition based on canonical duality theory is derived.…
Second-order optimality conditions of the bilevel programming problems are dependent on the second-order directional derivatives of the value functions or the solution mappings of the lower level problems under some regular conditions,…
It is well known that bilevel optimization problems are hard to solve both in theory and practice. In this paper, we highlight a further computational difficulty when it comes to solving bilevel problems with continuous but nonconvex lower…
Maintaining energy balance and economical operation is significant for multi-energy systems such as the energy hub. However, it is usually challenged by the frequently changing and unpredictable uncertainties at different timescales. Under…
Stochastic bilevel optimization finds widespread applications in machine learning, including meta-learning, hyperparameter optimization, and neural architecture search. To extend stochastic bilevel optimization to distributed data, several…
Optimization problems with discrete decisions are nonconvex and thus lack strong duality, which limits the usefulness of tools such as shadow prices and the KKT conditions. It was shown in Burer(2009) that mixed-binary quadratic programs…
Energy storage is expected to play an increasingly important role in mitigating variations that come along with the growing penetration of renewable energy. In this paper, we study the optimal bidding of an energy storage unit in a…
This work proposes an uncertainty-informed bid adjustment framework for integrating variable renewable energy sources (VRES) into electricity markets. This framework adopts a bilevel model to compute the optimal VRES day-ahead bids. It aims…
We study a bilevel \emph{max-max} optimization framework for principal-agent contract design, in which a principal chooses incentives to maximize utility while anticipating the agent's best response. This problem, central to moral hazard…
Nonconvexities in markets with discrete decisions and nonlinear constraints make efficient pricing challenging, often necessitating subsidies. A prime example is the unit commitment (UC) problem in electricity markets, where costly…
This paper presents a comprehensive analytical study of two competitive cognitive operators' spectrum leasing and pricing strategies, taking into account operators' heterogeneity in leasing costs and users' heterogeneity in transmission…
We consider bilevel linear problems, where the right-hand side of the lower level problems is stochastic. The leader has to decide in a here-and-now fashion, while the follower has complete information. In this setting, the leader's outcome…
This study develops a scalable co-optimization strategy for the joint bidding of cascaded hydropower, wind, and solar energy units, treated as a unified entity in the day-ahead market. Although hydropower flexibility can manage the…
This paper studies bilevel polynomial optimization problems. To solve them, we give a method based on polynomial optimization relaxations. Each relaxation is obtained from the Kurash-Kuhn-Tucker (KKT) conditions for the lower level…
Energy forecasting is an essential task in power system operations. Operators usually issue forecasts and leverage them to schedule energy dispatch ahead of time. However, forecast models are typically developed in a way that overlooks the…