Exploiting problem structure in derivative free optimization

A structured version of derivative-free random pattern search optimization algorithms is introduced which is able to exploit coordinate partially separable structure (typically associated with sparsity) often present in unconstrained and bound-constrained optimization problems. This technique improves performance by orders of magnitude and makes it possible to solve large problems that otherwise are totally intractable by … Read more

On geometrical properties of preconditioners in IPMs for classes of block-angular problems

One of the most efficient interior-point methods for some classes of block-angular structured problems solves the normal equations by a combination of Cholesky factorizations and preconditioned conjugate gradient for, respectively, the block and linking constraints. In this work we show that the choice of a good preconditioner depends on geometrical properties of the constraints structure. … Read more

Solving structured nonlinear least-squares and nonlinear feasibility problems with expensive functions

We present an algorithm for nonlinear least-squares and nonlinear feasibility problems, i.e. for systems of nonlinear equations and nonlinear inequalities, which depend on the outcome of expensive functions for which derivatives are assumed to be unavailable. Our algorithm combines derivative-free techniques with filter trust-region methods to keep the number of expensive function evaluations low and … Read more