This paper considers a bilevel program, which has many applications in practice. To develop effective numerical algorithms, it is generally necessary to transform the bilevel program into a single-level optimization problem. The most popular approach is to replace the lower-level program by its KKT conditions and then the bilevel program can be transformed into a … Read more
In the context of decentralized portfolio management, understanding how to distribute a fixed budget among decentralized intermediaries is a relevant question for financial investors. We consider the Nash bargaining partitioning for a class of decentralized investment problems, where intermediaries are in charge of the portfolio construction in heterogeneous local markets and act as risk/disutility minimizers. … Read more
These are lecture notes on bilevel optimization. The class of bilevel optimization problems is formally introduced and motivated using examples from different fields. Afterward, the main focus is on how to solve linear and mixed-integer linear bilevel optimization problems. To this end, we first consider various single-level reformulations of bilevel optimization problems with linear or … Read more
Poisoning attack is one of the attack types commonly studied in the field of adversarial machine learning. The adversary generating poison attacks is assumed to have access to the training process of a machine learning algorithm and aims to prevent the algorithm from functioning properly by injecting manipulative data while the algorithm is being trained. … Read more
Bilevel optimization is an increasingly important tool to model hierarchical decision making. However, the ability of modeling such settings makes bilevel problems hard to solve in theory and practice. In this paper, we add on the general difficulty of this class of problems by further incorporating convex black-box constraints in the lower level. For this … Read more
Forecasting and decision-making are generally modeled as two sequential steps with no feedback, following an open-loop approach. In this paper, we present application-driven learning, a new closed-loop framework in which the processes of forecasting and decision-making are merged and co-optimized through a bilevel optimization problem. We present our methodology in a general format and prove … Read more
The European gas market is organized as a so-called entry-exit system with the main goal to decouple transport and trading. To this end, gas traders and the transmission system operator (TSO) sign so-called booking contracts that grant capacity rights to traders to inject or withdraw gas at certain nodes up to this capacity. On a … Read more
In bilevel optimization, hierarchical optimization problems are considered in which two players – the leader and the follower – act and react in a non-cooperative and sequential manner. In many real-world applications, the leader may face a follower whose reaction deviates from the one expected by the leader due to some kind of bounded rationality. … Read more
Bilevel optimization is a field of mathematical programming in which some variables are constrained to be the solution of another optimization problem. As a consequence, bilevel optimization is able to model hierarchical decision processes. This is appealing for modeling real-world problems, but it also makes the resulting optimization models hard to solve in theory and … Read more
The survey highlights some of the research topics which have attracted attention in the last two decades within the area of mathematical optimization of multiple objective functions. We give insights into topics where a huge progress can be seen within the last years. We give short introductions to the specific sub-fields as well as some … Read more