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Bilevel optimization is a fundamental tool in hierarchical decision-making and has been widely applied to machine learning tasks such as hyperparameter tuning, meta-learning, and continual learning. While significant progress has been made…

Optimization and Control · Mathematics 2025-04-25 Nazanin Abolfazli , Sina Sharifi , Mahyar Fazlyab , Erfan Yazdandoost Hamedani

This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of problem to sections of feasible set by random subspaces (in general, manifolds) of low…

Optimization and Control · Mathematics 2023-03-28 Dmitry A. Pasechnyuk , Alexander Gornov

Bilevel programming has recently received a great deal of attention due to its abundant applications in many areas. The optimal value function approach provides a useful reformulation of the bilevel problem, but its utility is often limited…

Optimization and Control · Mathematics 2025-06-10 Jan Harold Alcantara , Akiko Takeda

There are much recent interests in solving noncovnex min-max optimization problems due to its broad applications in many areas including machine learning, networked resource allocations, and distributed optimization. Perhaps, the most…

Optimization and Control · Mathematics 2021-12-20 Thinh T. Doan

We consider the standard optimistic bilevel optimization problem, in particular upper- and lower-level constraints can be coupled. By means of the lower-level value function, the problem is transformed into a single-level optimization…

Optimization and Control · Mathematics 2019-12-17 Andreas Fischer , Alain B. Zemkoho , Shenglong Zhou

One fundamental problem when solving inverse problems is how to find regularization parameters. This article considers solving this problem using data-driven bilevel optimization, i.e. we consider the adaptive learning of the regularization…

Statistics Theory · Mathematics 2021-01-08 Neil K. Chada , Claudia Schillings , Xin T. Tong , Simon Weissmann

In this paper we consider large-scale composite optimization problems having the objective function formed as a sum of two terms (possibly nonconvex), one has (block) coordinate-wise Lipschitz continuous gradient and the other is…

Optimization and Control · Mathematics 2024-01-10 Flavia Chorobura , Ion Necoara

There is a recent surge of interest in nonconvex reformulations via low-rank factorization for stochastic convex semidefinite optimization problem in the purpose of efficiency and scalability. Compared with the original convex formulations,…

Optimization and Control · Mathematics 2018-02-27 Jinshan Zeng , Ke Ma , Yuan Yao

We study a class of algorithms for solving bilevel optimization problems in both stochastic and deterministic settings when the inner-level objective is strongly convex. Specifically, we consider algorithms based on inexact implicit…

Optimization and Control · Mathematics 2022-07-12 Michael Arbel , Julien Mairal

Bilevel programming has recently received attention in the literature due to its wide range of applications, including reinforcement learning and hyper-parameter optimization. However, it is widely assumed that the underlying bilevel…

Machine Learning · Computer Science 2024-10-11 Parvin Nazari , Ahmad Mousavi , Davoud Ataee Tarzanagh , George Michailidis

The majority of First Order methods for large-scale convex-concave saddle point problems and variational inequalities with monotone operators are proximal algorithms which at every iteration need to minimize over problem's domain X the sum…

Optimization and Control · Mathematics 2015-10-05 Bruce Cox , Anatoli Juditsky , Arkadi Nemirovski

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…

Machine Learning · Statistics 2024-12-10 Ieva Petrulionyte , Julien Mairal , Michael Arbel

Hierarchical optimization refers to problems with interdependent decision variables and objectives, such as minimax and bilevel formulations. While various algorithms have been proposed, existing methods and analyses lack adaptivity in…

Machine Learning · Computer Science 2025-10-27 Xiaochuan Gong , Jie Hao , Mingrui Liu

Bilevel optimization is widely applied in many machine learning tasks such as hyper-parameter learning, meta learning and reinforcement learning. Although many algorithms recently have been developed to solve the bilevel optimization…

Optimization and Control · Mathematics 2024-07-26 Feihu Huang

We propose a unified framework for estimating low-rank matrices through nonconvex optimization based on gradient descent algorithm. Our framework is quite general and can be applied to both noisy and noiseless observations. In the general…

Machine Learning · Statistics 2016-10-18 Lingxiao Wang , Xiao Zhang , Quanquan Gu

This work proposes an implementable proximal-type method for a broad class of optimization problems involving nonsmooth and nonconvex objective and constraint functions. In contrast to existing methods that rely on an ad hoc model…

Optimization and Control · Mathematics 2024-09-26 Gregorio M. Sempere , Welington de Oliveira , Johannes O. Royset

We consider a scalar objective minimization problem over the solution set of another optimization problem. This problem is known as simple bilevel optimization problem and has drawn a significant attention in the last few years. Our inner…

Optimization and Control · Mathematics 2018-09-18 Yekini Shehu , Phan Tu Vuong , Alain Zemkoho

A nonsmooth set-gradient ascent method is developed for moving finite approximation sets toward the Pareto front in multiobjective optimization. The method optimizes layered set indicators: a base indicator is evaluated on successive…

Optimization and Control · Mathematics 2026-05-14 Michael T. M. Emmerich

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…

Optimization and Control · Mathematics 2018-02-08 Saeed Ghadimi , Mengdi Wang

We propose a proximal variable smoothing algorithm for a nonsmooth optimization problem whose cost function is the sum of three functions including a weakly convex composite function. The proposed algorithm has a single-loop structure…

Optimization and Control · Mathematics 2025-06-09 Keita Kume , Isao Yamada