Mikhail V. Solodov

A doubly stabilized bundle method for nonsmooth convex optimization

Categories Convex and Nonsmooth Optimization, Nonsmooth Optimization Tags , ,

We propose a bundle method for minimizing nonsmooth convex functions that combines both the level and the proximal stabilizations. Most bundle algorithms use a cutting-plane model of the objective function to formulate a subproblem whose solution gives the next iterate. Proximal bundle methods employ the model in the objective function of the subproblem, while level … Read more

A Class of Dantzig-Wolfe Type Decomposition Methods for Variational Inequality Problems

Categories Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization Tags ,

We consider a class of decomposition methods for variational inequalities, which is related to the classical Dantzig–Wolfe decomposition of linear programs. Our approach is rather general, in that it can be used with set-valued or nonmonotone operators, as well as various kinds of approximations in the subproblems of the functions and derivatives in the single-valued … Read more