Bi-Level Optimization (BLO) is originated from the area of economic game theory and then
introduced into the optimization community. BLO is able to handle problems with a …

In this paper we study convex bilevel optimization problems for which the inner level
consists of minimization of the sum of smooth and nonsmooth functions. The outer level aims …

We consider a scalar objective minimization problem over the solution set of another
optimization problem. This problem is known as a simple bilevel optimization problem and …

Purpose: To describe and mathematically validate the superiorization methodology, which is
a recently developed heuristic approach to optimization, and to discuss its applicability to …

The projected subgradient method for constrained minimization repeatedly interlaces
subgradient steps for the objective function with projections onto the feasible region, which …

In this paper, we propose three kinds of inertial approximation methods based on the
proximal gradient algorithm to accelerate the convergence of the algorithm for solving …

We study a class of bilevel convex optimization problems where the goal is to find the
minimizer of an objective function in the upper level, among the set of all optimal solutions of …

This paper introduces and studies the convergence properties of a new class of explicit
epsilon-subgradient methods for the task of minimizing a convex function over a set of …

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 …

Many scientific, engineering and medical applications of image analysis use constrained
optimization, with the constraints arising from the desire to produce a solution that is …