Project
overview
Aims
and scope
The
research project purpose is to study some
meaningful real-world problems of high
computational complexity in Nonlinear
Optimization; the computational power of
parallel architectures and the novel
Numerical Analysis methods will be
challenged on these problems. For some
methods, the analysis will go on up to
the implementation of computational kernels
in the context of the parallel software. The
following prototypical problems will be
considered:
- Large
Scale Optimization Problems:
optimal control problems,
identification problems, image
restoration problems; for these
problems, sequential quadratic
programming methods, interior
point methods, penalty methods,
projection methods and
regularization methods will be
analyzed;
- Global
Optimization Problems:
for global optimization of
Lipschitz functions, parallel
methods based on the space
filling curves will be analyzed.
One
of the primary goal of this analysis is the
implementation of parallel computational
kernels, whose robustness and effectiveness
be proved on a certain platform. They would
be used as "building-blocks"
for the construction of distributed
applications that need the support of grid
computing. Special attention will be devoted
to the contributions about the theoretical
convergence of the methods and their
numerical stability. Software tools for an
automatic error control in the algorithms
will be designed. The effectiveness of the
developed methods for the solution of
the considered problems will be evaluated on
some 'model problems'; this production
of "benchmark" of the new methods
on significant 'model problems' is one
of the expected results of the project.
Keywords
Parallel
Computing, Large Scale Optimization, Local
and Global Optimization, Nonlinear
Programming, Analysis of Parallel Algorithms,
Parallel Software.
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