Related papers: Newton-type Multilevel Optimization Method
Multilevel techniques are efficient approaches for solving the large linear systems that arise from discretized partial differential equations and other problems. While geometric multigrid requires detailed knowledge about the underlying…
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…
First-order methods for solving convex optimization problems have been at the forefront of mathematical optimization in the last 20 years. The rapid development of this important class of algorithms is motivated by the success stories…
Machine Learning models incorporating multiple layered learning networks have been seen to provide effective models for various classification problems. The resulting optimization problem to solve for the optimal vector minimizing the…
Bilevel Optimization Programming is used to model complex and conflicting interactions between agents, for example in Robust AI or Privacy-preserving AI. Integrating bilevel mathematical programming within deep learning is thus an essential…
Hyperparameter tuning is an active area of research in machine learning, where the aim is to identify the optimal hyperparameters that provide the best performance on the validation set. Hyperparameter tuning is often achieved using naive…
Bilevel optimization, a well-established field for modeling hierarchical decision-making problems, has recently intersected with sustainability studies and practices, resulting in a series of works focusing on bilevel optimization problems…
Both bilevel and robust optimization are established fields of mathematical optimization and operations research. However, only until recently, the similarities in their mathematical structure has neither been studied theoretically nor…
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…
The object of the present paper is to extend the third-order iterative method for solving nonlinear equations into systems of nonlinear equations. Since our motive is to develop the method which improve the order of convergence of Newton's…
The objective of this paper is to introduce and demonstrate a robust method for multi-constrained topology optimization. The method is derived by combining the topological sensitivity with the classic augmented Lagrangian formulation. The…
Bilevel Optimization has experienced significant advancements recently with the introduction of new efficient algorithms. Mirroring the success in single-level optimization, stochastic gradient-based algorithms are widely used in bilevel…
Computing at the exascale level is expected to be affected by a significantly higher rate of faults, due to increased component counts as well as power considerations. Therefore, current day numerical algorithms need to be reexamined as to…
In practice, optimization tasks have some structure that allows developing new algorithms for every problem with faster convergence rates. Using the structure of optimization tasks, we can propose algorithms with more optimistic convergence…
We review some recent learning approaches in variational imaging, based on bilevel optimisation, and emphasize the importance of their treatment in function space. The paper covers both analytical and numerical techniques. Analytically, we…
In this paper, a globally convergent Newton-type proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…
We introduce a framework based on bilevel programming that unifies gradient-based hyperparameter optimization and meta-learning. We show that an approximate version of the bilevel problem can be solved by taking into explicit account the…
Topology optimization problems often support multiple local minima due to a lack of convexity. Typically, gradient-based techniques combined with continuation in model parameters are used to promote convergence to more optimal solutions;…
The distributed optimization problem is set up in a collection of nodes interconnected via a communication network. The goal is to find the minimizer of a global objective function formed by the addition of partial functions locally known…
A novel multiscale consensus-based optimization (CBO) algorithm for solving bi- and tri-level optimization problems is introduced. Existing CBO techniques are generalized by the proposed method through the employment of multiple interacting…