Related papers: Bilevel Programming Problems: A view through Set-v…
In this paper we study constraint qualifications and optimality conditions for bilevel programming problems. We strive to derive checkable constraint qualifications in terms of problem data and applicable optimality conditions. For 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…
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…
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…
It is well-known that coupling constraints in linear bilevel optimization can lead to disconnected feasible sets, which is not possible without coupling constraints. However, there is no difference between linear bilevel problems with and…
Bilevel reinforcement learning (RL), which features intertwined two-level problems, has attracted growing interest recently. The inherent non-convexity of the lower-level RL problem is, however, to be an impediment to developing bilevel…
In this paper, we propose a combined approach with second-order optimality conditions of the lower level problem to study constraint qualifications and optimality conditions for bilevel programming problems. The new method is inspired by…
In this paper, we study a class of bilevel optimization program (BP), where the feasible set of the lower level program is independent of the upper level variable. For bilevel programs it is known that the first order approach requires the…
This work formulates the machine learning mechanism as a bi-level optimization problem. The inner level optimization loop entails minimizing a properly chosen loss function evaluated on the training data. This is nothing but the…
We consider discrete bilevel optimization problems where the follower solves an integer program with a fixed number of variables. Using recent results in parametric integer programming, we present polynomial time algorithms for pure and…
Learning to Optimize (L2O) is a subfield of machine learning (ML) in which ML models are trained to solve parametric optimization problems. The general goal is to learn a fast approximator of solutions to constrained optimization problems,…
This paper studies the joint optimization of edge node activation and resource pricing in edge computing, where an edge computing platform provides heterogeneous resources to accommodate multiple services with diverse preferences. We cast…
In optimization-based image restoration models, the correct selection of hyperparameters is crucial for achieving superior performance. However, current research typically involves manual tuning of these hyperparameters, which is highly…
Bilevel optimization is an important class of optimization problems where one optimization problem is nested within another. While various methods have emerged to address unconstrained general bilevel optimization problems, there has been a…
Variational regularization methods are commonly used to approximate solutions of inverse problems. In recent years, model-based variational regularization methods have often been replaced with data-driven ones such as the fields-of-expert…
In this paper, we study the regularity assumptions commonly adopted in bilevel optimization with constrained lower-level problems, including the linear independence constraint qualification, the strict complementary slackness condition, and…
In this paper, we consider a bilevel polynomial optimization problem where the objective and the constraint functions of both the upper and the lower level problems are polynomials. We present methods for finding its global minimizers and…
In this article we intend to develop a simple and implementable algorithm for minimizing a convex function over the solution set of another convex optimization problem. Such a problem is often referred to as a simple bilevel programming…
We consider class of equilibrium models including the implicit Walras supply-demand and competitive models. Such a model in this class, in general, is ill-posed. We formulate such a model in the form a variational inequality having certain…
Convex optimization problems arising in applications often have favorable objective functions and complicated constraints, thereby precluding first-order methods from being immediately applicable. We describe an approach that exchanges the…