Related papers: BilevelJuMP.jl: Modeling and Solving Bilevel Optim…
In this work, we propose derivative-free framework for bilevel optimization. We consider both the upper and lower-level problems with bound constraints on the variables, as well as general nonlinear constraints, assuming that first-order…
This article introduces new acceleration methods for fixed-point iterations. Extrapolations are computed using two or three mappings alternately and a new type of step length is proposed with good properties for nonlinear applications. The…
Agent based modelling is a simulation method in which autonomous agents interact with their environment and one another, given a predefined set of rules. It is an integral method for modelling and simulating complex systems, such as…
Geometric computing with chain complexes allows for the computation of the whole chain of linear spaces and (co)boundary operators generated by a space decomposition into a cell complex. The space decomposition is stored and handled with…
Algorithm NCL is designed for general smooth optimization problems where first and second derivatives are available, including problems whose constraints may not be linearly independent at a solution (i.e., do not satisfy the LICQ). It is…
Proprietary closed-source software is still the norm in advanced process control. Transparency and reproducibility are key aspects of scientific research. Free and open-source toolkit can contribute to the development, sharing and…
MultiPrecisionArrays.jl is a Julia package. This package provides data structures and solvers for several variants of iterative refinement. It will become much more useful when half precision (aka Float16) is fully supported in LAPACK/BLAS.…
Bi-level optimization, especially the gradient-based category, has been widely used in the deep learning community including hyperparameter optimization and meta-knowledge extraction. Bi-level optimization embeds one problem within another…
Recently, bi-level optimization (BLO) has taken center stage in some very exciting developments in the area of signal processing (SP) and machine learning (ML). Roughly speaking, BLO is a classical optimization problem that involves two…
Combinatorial optimization (CO) layers in machine learning (ML) pipelines are a powerful tool to tackle data-driven decision tasks, but they come with two main challenges. First, the solution of a CO problem often behaves as a piecewise…
There are plenty of excellent plotting libraries. Each excels at a different use case: one is good for printed 2D publication figures, the other at interactive 3D graphics, a third has excellent L A TEX integration or is good for creating…
Biclustering is a data mining technique which searches for local patterns in numeric tabular data with main application in bioinformatics. This technique has shown promise in multiple areas, including development of biomarkers for cancer,…
Scheduling problems requires to explicitly account for control considerations in their optimisation. The literature proposes two traditional ways to solve this integrated problem: hierarchical and monolithic. The monolithic approach ignores…
Optimization problems are pervasive across various sectors, from manufacturing and distribution to healthcare. However, most such problems are still solved heuristically by hand rather than optimally by state-of-the-art solvers, as the…
This article studies Gauss-Newton-type methods for over-determined systems to find solutions to bilevel programming problems. To proceed, we use the lower-level value function reformulation of bilevel programs and consider necessary…
We first show a simple but striking result in bilevel optimization: unconstrained $C^\infty$ smooth bilevel programming is as hard as general extended-real-valued lower semicontinuous minimization. We then proceed to a worst-case analysis…
Hierarchical optimization architectures are used in power systems to manage disturbances and phenomena that arise at multiple spatial and temporal scales. We present a graph modeling abstraction for representing such architectures and an…
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…
Bilevel optimization enjoys a wide range of applications in emerging machine learning and signal processing problems such as hyper-parameter optimization, image reconstruction, meta-learning, adversarial training, and reinforcement…
Optimization problems are pervasive in sectors from manufacturing and distribution to healthcare. However, most such problems are still solved heuristically by hand rather than optimally by state-of-the-art solvers because the expertise…