Note on a method of conjugate subgradients for minimizing nondifferentiable functions

Note on an extension of "Davidon" methods to nondifferentiable functions

1. This note summarizes a paper [4] to appear in full elsewhere. It presents an algorithm for the minimization of a general (not necessarily differentiable) convex function. Its central idea is the construction of descent directions as projections of the origin onto the convex hull of previously calculated subgradients as long as satisfactory progress can be made. Using projection to obtain a d...

An effective optimization algorithm for locally nonconvex Lipschitz functions based on mollifier subgradients

Use of Differentiable and Nondifferentiable Optimization Algorithms for Variational Data Assimilation with Discontinuous Cost Functions

Cost functions formulated in four-dimensional variational data assimilation (4DVAR) are nonsmooth in the presence of discontinuous physical processes (i.e., the presence of ‘‘on–off’’ switches in NWP models). The adjoint model integration produces values of subgradients, instead of gradients, of these cost functions with respect to the model’s control variables at discontinuous points. Minimiza...

Incremental Subgradient Methods for Nondifferentiable Optimization

We consider a class of subgradient methods for minimizing a convex function that consists of the sum of a large number of component functions. This type of minimization arises in a dual context from Lagrangian relaxation of the coupling constraints of large scale separable problems. The idea is to perform the subgradient iteration incrementally, by sequentially taking steps along the subgradien...

Incremental Subgradient Methods 1 for Nondifferentiable Optimization

We consider a class of subgradient methods for minimizing a convex function that consists of the sum of a large number of component functions. This type of minimization arises in a dual context from Lagrangian relaxation of the coupling constraints of large scale separable problems. The idea is to perform the subgradient iteration incrementally, by sequentially taking steps along the subgradien...