Nondifferentiable Optimization

TL;DR: This paper is a review of Lagrangian relaxation based on what has been learned in the last decade and has led to dramatically improved algorithms for a number of important problems in the areas of routing, location, scheduling, assignment and set covering.

TL;DR: A number of variants of incremental subgradient methods for minimizing a convex function that consists of the sum of a large number of component functions are established, including some that are stochastic.

TL;DR: This work presents a subgradient algorithm for generating approximate saddle points and provides per-iteration convergence rate estimates on the constructed solutions, and focuses on Lagrangian duality, where it is shown this algorithm is particularly well-suited for problems where the subgradient of the dual function cannot be evaluated easily.

TL;DR: This work provides estimates on the primal infeasibility and primal suboptimality of the generated approximate primal solutions and provides a basis for analyzing the trade-offs between the desired level of error and the selection of the stepsize value.