Related papers: A novel strong duality-based reformulation for tri…
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…
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…
As renewable energy integration, sector coupling, and spatiotemporal detail increase, energy system optimization models grow in size and complexity, often pushing solvers to their performance limits. This systematic review explores…
As the world is transitioning towards highly renewable energy systems, advanced tools are needed to analyze such complex networks. Energy system design is, however, challenged by real-world objective functions consisting of a blurry mix of…
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…
We discuss the multilevel control problem for linear dynamical systems, consisting in designing a piece-wise constant control function taking values in a finite-dimensional set. In particular, we provide a complete characterization of…
A strong-to-weak-coupling duality is established for the nonequilibrium interacting resonant-level model, describing tunneling through a single spinless level, capacitively coupled to two leads by a contact interaction. For large capacitive…
Hyperparameter tuning is an important task of machine learning, which can be formulated as a bilevel program (BLP). However, most existing algorithms are not applicable for BLP with non-smooth lower-level problems. To address this, we…
Network segmentation of a power grid's communication system is one way to make the grid more resilient to cyber attacks. We develop a novel trilevel programming model to optimally segment a grid communication system, taking into account the…
Distributed energy resources (DER) provide significant value for renewable energy integration in modern power grids. However, unlocking this value requires complex design and coordination. This paper focuses on the emerging {\em transactive…
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…
We investigate relaxations for a class of discrete bilevel programs where the interaction constraints linking the leader and the follower are linear. Our approach reformulates the upper-level optimality constraints by projecting the…
Bilevel programming problems frequently arise in real-world applications across various fields, including transportation, economics, energy markets and healthcare. These problems have been proven to be NP-hard even in the simplest form with…
Many discrete optimization problems are amenable to constrained shortest-path reformulations in an extended network space, a technique that has been key in convexification, bound strengthening, and search. In this paper, we propose a…
Bilevel programming can be used to formulate many problems in the field of power systems, such as strategic bidding. However, common reformulations of bilevel problems to mixed-integer linear programs make solving such problems hard, which…
Coordinating the operation of units at the interface between heat and electricity systems, such as combined heat and power plants and heat pumps, is essential to reduce inefficiencies in each system and help achieve a cost-effective and…
We consider a two-stage market mechanism for trading electricity including renewable generation as an alternative to the widely used multi-settlement market structure. The two-stage market structure allows for recourse decisions by the…
In the present article we propose a mixed-integer approximation of adjustable-robust optimization (ARO) problems, that have both, continuous and discrete variables on the lowest level. As these trilevel problems are notoriously hard to…
Transitioning to a Circular Economy requires policies to drive sustainable practices. This study proposes a bilevel optimization framework to evaluate the combined use of carbon taxes and subsidies in promoting circular supply chains under…
Differential equations (DE) constrained optimization plays a critical role in numerous scientific and engineering fields, including energy systems, aerospace engineering, ecology, and finance, where optimal configurations or control…