  General purpose optimization techniques can be used to solve many problems in
engineering computations, although their cost is often prohibitive when the
number of degrees of freedom is very large. We describe a multilevel approach
to speed up the computation of the solution of a large-scale optimization
problem by a given optimization technique. By embedding the problem within
Harten's Multiresolution Framework (MRF), we set up a procedure that leads to
the desired solution, after the computation of a finite sequence of sub-optimal
solutions, which solve auxiliary optimization problems involving a smaller
number of variables. For convex optimization problems having smooth solutions,
we prove that the distance between the optimal solution and each sub-optimal
approximation is related to the accuracy of the interpolation technique used
within the MRF and analyze its relation with the performance of the proposed
algorithm. Several numerical experiments confirm that our technique provides a
computationally efficient strategy that allows the end user to treat both the
optimizer and the objective function as black boxes throughout the optimization
process.
