Related papers: A Brief Introduction to Robust Bilevel Optimizatio…
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…
Real-world problems typically require the simultaneous optimization of several, often conflicting objectives. Many of these multi-objective optimization problems are characterized by wide ranges of uncertainties in their decision variables…
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…
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…
This paper firstly proposes a convex bilevel optimization paradigm to formulate and optimize popular learning and vision problems in real-world scenarios. Different from conventional approaches, which directly design their iteration schemes…
Motivated by emerging applications in wireless sensor networks and large-scale data processing, we consider distributed optimization over directed networks where the agents communicate their information locally to their neighbors to…
In this paper, we develop a two-stage data-driven approach to address the adjustable robust optimization problem, where the uncertainty set is adjustable to manage infeasibility caused by significant or poorly quantified uncertainties. In…
In multi-robot systems, achieving coordinated missions remains a significant challenge due to the coupled nature of coordination behaviors and the lack of global information for individual robots. To mitigate these challenges, this paper…
This paper reviews recent advances in the field of optimization under uncertainty via a modern data lens, highlights key research challenges and promise of data-driven optimization that organically integrates machine learning and…
This paper delves into the challenging issues in uncertain multi-objective optimization, where uncertainty permeates nonsmooth nonconvex objective and constraint functions. In this context, we investigate highly robust (weakly efficient)…
This paper presents a novel robust trajectory optimization method for constrained nonlinear dynamical systems subject to unknown bounded disturbances. In particular, we seek optimal control policies that remain robustly feasible with…
In this paper, we study a class of bilevel programming problem where the inner objective function is strongly convex. More specifically, under some mile assumptions on the partial derivatives of both inner and outer objective functions, we…
In this letter, we consider a bilevel optimization problem in which the outer-level objective function is strongly convex, whereas the inner-level problem consists of a finite sum of convex functions. Bilevel optimization problems arise in…
Inspired by multigrid methods for linear systems of equations, multilevel optimization methods have been proposed to solve structured optimization problems. Multilevel methods make more assumptions regarding the structure of the…
Optimizing decision problems under uncertainty can be done using a variety of solution methods. Soft computing and heuristic approaches tend to be powerful for solving such problems. In this overview article, we survey Evolutionary…
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…
Our goal is to build robust optimization problems for making decisions based on complex data from the past. In robust optimization (RO) generally, the goal is to create a policy for decision-making that is robust to our uncertainty about…
Real-world optimization problems often do not just involve multiple objectives but also uncertain parameters. In this case, the goal is to find Pareto-optimal solutions that are robust, i.e., reasonably good under all possible realizations…
Bilevel optimization provides a powerful framework for modelling hierarchical decision-making systems. This work presents a sensitivity-based algorithm that addresses the bilevel structure directly by treating the lower-level optimal…
Bilevel optimization recently has attracted increased interest in machine learning due to its many applications such as hyper-parameter optimization and meta learning. Although many bilevel methods recently have been proposed, these methods…