Related papers: Bilevel optimization with sustainability perspecti…
The increasing availability of massive data sets poses a series of challenges for machine learning. Prominent among these is the need to learn models under hardware or human resource constraints. In such resource-constrained settings, a…
In this paper we study an infinite-horizon persistent monitoring problem in a two-dimensional mission space containing a finite number of statically placed targets, at each of which we assume a constant rate of uncertainty accumulation.…
We consider the convex bilevel optimization problem, also known as simple bilevel programming. There are two challenges in solving convex bilevel optimization problems. Firstly, strong duality is not guaranteed due to the lack of Slater…
Some recent works in machine learning and computer vision involve the solution of a bi-level optimization problem. Here the solution of a parameterized lower-level problem binds variables that appear in the objective of an upper-level…
Bilevel optimization problems involve two nested objectives, where an upper-level objective depends on a solution to a lower-level problem. When the latter is non-convex, multiple critical points may be present, leading to an ambiguous…
Energy forecasting is an essential task in power system operations. Operators usually issue forecasts and leverage them to schedule energy dispatch ahead of time. However, forecast models are typically developed in a way that overlooks the…
In bilevel optimization problems, a leader and a follower make their decisions in a hierarchy, and both decisions may influence each other. Usually one assumes that both players have full knowledge also of the other player's data. In a more…
Winter road maintenance is critical for ensuring public safety and reducing environmental impacts, yet existing methods struggle to manage large-scale routing problems effectively and mostly reply on human decision. This study presents a…
The goal of coreset selection in supervised learning is to produce a weighted subset of data, so that training only on the subset achieves similar performance as training on the entire dataset. Existing methods achieved promising results in…
In this work we derive a second-order approach to bilevel optimization, a type of mathematical programming in which the solution to a parameterized optimization problem (the "lower" problem) is itself to be optimized (in the "upper"…
This work uniquely combines an affine linear decision rule known from adjustable robustness with min-max-regret robustness. By doing so, the advantages of both concepts can be obtained with an adjustable solution that is not…
This paper proposes a Real-Time Market (RTM) platform for an aggregator and its corresponding prosumers to participate in the electricity wholesale market. The proposed energy market platform is modeled as a bilevel optimization problem…
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…
Near-optimality robustness extends multilevel optimization with a limited deviation of a lower level from its optimal solution, anticipated by higher levels. We analyze the complexity of near-optimal robust multilevel problems, where…
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…
With the growing attention towards developing the multimodal transport system to enhance urban mobility, there is an increasing need to construct new, rebuild or expand existing infrastructure to facilitate existing and accommodate newly…
Current state-of-the-art solution techniques for solving bilevel optimization problems either assume strong problem regularity criteria or are computationally intractable. In this paper we address power system problems of bilevel structure,…
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;…
Inverse problems are key issues in several scientific areas, including signal processing and medical imaging. Data-driven approaches for inverse problems aim for learning model and regularization parameters from observed data samples, and…
We present an efficient optimization framework that solves trajectory optimization problems by decoupling state variables from timing variables, thereby decomposing a challenging nonlinear programming (NLP) problem into two easier…