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The performance of evolutionary algorithms can be heavily undermined when constraints limit the feasible areas of the search space. For instance, while Covariance Matrix Adaptation Evolution Strategy is one of the most efficient algorithms…

We study a class of bilevel convex optimization problems where the goal is to find the minimizer of an objective function in the upper level, among the set of all optimal solutions of an optimization problem in the lower level. A wide range…

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…

In this article we provide a comprehensive review of the different evolutionary algorithm techniques used to address multimodal optimization problems, classifying them according to the nature of their approach. On the one hand there are…

Bilevel optimization has been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel optimization problem, where the lower-level optimization problem is convex with…

In this paper, we study a class of stochastic bilevel optimization problems, also known as stochastic simple bilevel optimization, where we minimize a smooth stochastic objective function over the optimal solution set of another stochastic…

The rapid advances in the field of optimization methods in many pure and applied science pose the difficulty of keeping track of the developments as well as selecting an appropriate technique that best suits the problem in-hand. From a…

The literature on pessimistic linear bilevel optimization with coupling constraints is rather scarce and it has been common sense that these problems are harder to tackle than pessimistic bilevel problems without coupling constraints. In…

Chance constraints are a valuable tool for the design of safe decisions in uncertain environments; they are used to model satisfaction of a constraint with a target probability. However, because of possible non-convexity and non-smoothness,…

In this paper, we propose a procedure for designing controlled test problems for single-objective bilevel optimization. The construction procedure is flexible and allows its user to control the different complexities that are to be included…

Bilevel optimization reveals the inner structure of otherwise oblique optimization problems, such as hyperparameter tuning, neural architecture search, and meta-learning. A common goal in bilevel optimization is to minimize a…

In this paper, we focus on simple bilevel optimization problems, where we minimize a convex smooth objective function over the optimal solution set of another convex smooth constrained optimization problem. We present a novel bilevel…

Bilevel learning has gained prominence in machine learning, inverse problems, and imaging applications, including hyperparameter optimization, learning data-adaptive regularizers, and optimizing forward operators. The large-scale nature of…

Bilevel optimization poses a significant computational challenge due to its nested structure, where each upper-level candidate solution requires solving a corresponding lower-level problem. While evolutionary algorithms (EAs) are effective…

Bilevel optimization is a field of significant theoretical and practical interest, yet solving such optimization problems remains challenging. Evolutionary methods have been employed to address these problems in the black-box setting;…

The chance-constrained knapsack problem is a variant of the classical knapsack problem where each item has a weight distribution instead of a deterministic weight. The objective is to maximize the total profit of the selected items under…

Bilevel optimization has recently attracted growing interests due to its wide applications in modern machine learning problems. Although recent studies have characterized the convergence rate for several such popular algorithms, it is still…

Constrained submodular optimization problems play a key role in the area of combinatorial optimization as they capture many NP-hard optimization problems. So far, Pareto optimization approaches using multi-objective formulations have been…

This paper considers the simple bilevel optimization (SBO) problem, which minimizes a composite convex function over the optimal solution set of another composite convex minimization problem. We first show that this bilevel problem is…

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…