In this paper, we propose the Bi-Sub-Gradient (Bi-SG) method, which is a generalization of
the classical sub-gradient method to the setting of convex bi-level optimization problems …

Simple bilevel problems are optimization problems in which we want to find an optimal
solution to an inner problem that minimizes an outer objective function. Such problems …

We propose a new framework for solving the convex bilevel optimization problem, where
one optimizes a convex objective over the optimal solutions of another convex optimization …

When faced with multiple minima of an inner-level convex optimization problem, the convex
bilevel optimization problem selects an optimal solution which also minimizes an auxiliary …

We present two approximate versions of the proximal subgradient method for minimizing the
sum of two convex functions (not necessarily differentiable). At each iteration, the algorithms …

In this article we focus on algorithms for solving simple bilevel programming problems.
Simple bilevel problems consist of minimizing a convex function over the solution set of …

The deployment of advanced information and communication technologies necessitates
considering new security threats, such as distributed denial of service attacks and malware …

A wide range of applications arising in machine learning and signal processing can be cast
as convex optimization problems. These problems are often ill-posed, ie, the optimal …

Bi-level optimization problems, where one wishes to find the global minimizer of an upper-
level objective function over the globally optimal solution set of a lower-level objective, arise …

In this paper, we focus on simple bilevel optimization problems, where we minimize a
convex smooth objective function over the optimal solution set of another convex smooth …