A first order method for finding minimal norm-like solutions of convex optimization problems
We consider a general class of convex optimization problems in which one seeks to minimize a strongly convex function over a closed and convex set which is by itself an optimal set of another convex problem. We introduce a gradient-based method, called the minimal norm gradient method, for solving this class of problems, and establish the convergence of the sequence generated by the algorithm as well as a rate of convergence of the sequence of function values. The paper ends with several illustrating numerical examples.
bilevel optimization complexity analysis convex minimization minimal norm solution 90c05 90c25 90c30 65k05 65f22