Related papers: Directional necessary optimality conditions for bi…

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 propose a new approach to solving bilevel optimization problems, intermediate between solving full-system optimality conditions with a Newton-type approach, and treating the inner problem as an implicit function. The overall idea is to…

The authors' paper in Optimization 63 (2014), 505-533, see Ref. [5], was the first one to provide detailed optimality conditions for pessimistic bilevel optimization. The results there were based on the concept of the two-level optimal…

Here, necessary optimal condition for Optimistic Bilevel programming problem is obtained in Asplund spaces. Also we have got necessary optimal conditions in finite dimensional spaces, by assuming differentiability on the given functions.

Second-order optimality conditions for vector nonlinear programming problems with inequality constraints are studied in this paper. We introduce a new second-order constraint qualification, which includes Mangasarian-Fromovitz constraint…

Bilevel linear programming (LP) is one of the simplest classes of bilevel optimization problems, yet it is known to be NP-hard in general. Specifically, determining whether the optimal objective value of a bilevel LP is at least as good as…

Bilevel learning refers to machine learning problems that can be formulated as bilevel optimization models, where decisions are organized in a hierarchical structure. This paradigm has recently gained considerable attention in machine…

We consider optimization problems with a disjunctive structure of the constraints. Prominent examples of such problems are mathematical programs with equilibrium constraints or vanishing constraints. Based on the concepts of directional…

We consider a multiobjective bilevel optimization problem with vector-valued upper- and lower-level objective functions. Such problems have attracted a lot of interest in recent years. However, so far, scalarization has appeared to be the…

We address the problem of optimal scale-dependent parameter learning in total variation image denoising. Such problems are formulated as bilevel optimization instances with total variation denoising problems as lower-level constraints. For…

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…

As a starting point of our research, we show that, for a fixed order $\gamma\geq 1$, each local minimizer of a rather general nonsmooth optimization problem in Euclidean spaces is either M-stationary in the classical sense (corresponding to…

Bilevel optimization and bilevel minimax optimization have recently emerged as unifying frameworks for a range of machine-learning tasks, including hyperparameter optimization and reinforcement learning. The existing literature focuses on…

Variational regularization is commonly used to solve linear inverse problems, and involves augmenting a data fidelity by a regularizer. The regularizer is used to promote a priori information and is weighted by a regularization parameter.…

Bilevel optimization has found extensive applications in modern machine learning problems such as hyperparameter optimization, neural architecture search, meta-learning, etc. While bilevel problems with a unique inner minimal point (e.g.,…

Bilevel programming has recently received a great deal of attention due to its abundant applications in many areas. The optimal value function approach provides a useful reformulation of the bilevel problem, but its utility is often limited…

In this paper, we introduce a new functional point of view on bilevel optimization problems for machine learning, where the inner objective is minimized over a function space. These types of problems are most often solved by using methods…

Bilevel optimization is a key framework in hierarchical decision-making, where one problem is embedded within the constraints of another. In this work, we propose a control-theoretic approach to solving bilevel optimization problems. Our…

In many applications, including Stackelberg games, machine learning, and power systems \cite{Mackay2018Selftuning,Heinrich1952The,Wang2021Bi-Level}, the decisions in a minimax optimization problem can be constrained by a solution to an…

Bilevel optimization minimizes an objective function, defined by an upper-level problem whose feasible region is the solution of a lower-level problem. We study the oracle complexity of finding an $\epsilon$-stationary point with…