Third year
research advances
Research
Advances
Note: due to an excessive delay of the Italian University and Research Ministry (MIUR)
in providing the funds, the project activities are slowed.
Thus an extension of 12 months of the project has been requested and obtained.
Perturbed
dumped Newton and SQP-IP methods for
discretized optimal control problems
Researchers.
V. Ruggiero, S. Bonettini, F. Tinti.
Advances.
For the nonlinear systems of equations with restriction on the sign of the
variables, arising from NLP problems, all the theoretical and numerical results
on the inexact IP methods have been collected by the research group
[BGR-06].
In [BR-05]
various iterative solvers of the inner linear KKT system (Hestenes,
preconditioned conjugate gradient
with indefinite blocks preconditioner combined with regularization
techniques) have been analyzed.
For the numerical solution of the Variational Inequalities (VI),
a semismooth Newton scheme is proposed in combination with
iterative inner solvers with adaptive stopping rule; this approach
leads to a converging inexact semismooth
Newton method. In this scheme, for large-scale, sparse problems the LSQR
method with an incomplete LU block
preconditioner can be used. In this case, only submatrices with reduced
size have to be factorized directly
[RT-06].
[Top]
Variable
projection methods: a successful approach to
SVMs and large-scale simply constrained QP
Researchers.
L. Zanni, G. Zanghirati.
Advances.
In the machine learning context, new decomposition
techniques based on the projected gradient methods for the SVMs have been developed.
The effectiveness of the new algorithms for the projection on the feasible region
consisting in one linear equality constraint and box constraints have been studied.
These algorithms have been evaluated in the class of projected gradient methods,
in serial as well as in parallel environments
[SZZ-05b,
Z-06],
and they have been employed in a new parallel version of the decomposition
software gpdt
(dm.unife.it/gpdt).
[Top]
Adaptive
diagonal space-filling curves: linking
geometric Lipschitz and Bayesian
approaches for non-differentiable global
optimization
Researchers.
Ya. D. Sergeyev, D. Lera, D. Kvasov.
Advances.
The design of algorithms for the global constrained optimization where
the object function and the constraints
are "block-box" multiextremal Lipschitz functions, not necessarily
differentiable, has been developed.
In [S-06a,
SKK-07b]
unidimensional problems with nondifferentiable
multiextremal constraints with a
feasible region given by nonconvex disjoint subregions
have been considered. For the index scheme methods,
support functions without additional variables and
penalty coefficients have been proposed.
In [SK-06,
SK-04], for multidimensional
problems with box constraints, a new technique for the
estimation of the Lipschitz constant and
for the partitioning of the research domain, with a different
balancing the local and global phases in the optimum
search have been employed.
The global optimization techniques have been employed to the
solution of a practical problem arising from the
control theory [CPS-06].
[Top]
Symbolic
calculus and parallel computing for error
propagation automatic control
Researchers.
G. Spaletta.
Advances.
In the Mathematica framework, functionalities for the derivation and the analysis
of numerical solvers both for differential equations and for medical and
astronomic data approximation have been carried out
[SC-05,
SC-06].
For both the problems types, a suitable accuracy is required for the
obtained approximation, maintaining the qualitative
characteristics of the solution with a low computational cost.
The possibility of using a variable
precision, as for example with the Significant Arithmetics,
becomes very important
[SS-05a].
[Top]
Parallel
domain decomposition techniques for
space-variant blurred images restoration
Researchers.
F. Zama, E. Loli Piccolomini, G. Landi.
Advances.
In [LZ-06]
a method based on the active set has
been introduced for determining the regularized Tikhonov solutions
with positivity constraints on the solutions.
This method showed to be effective in the removing of the oscillations which
are characteristics of the solution
regularized with the Tikhonov method. Even if this method is suitable
for medium size problems, the computational
cost can be reduced by inexactly solving the subproblems,
in order to obtain regularized solutions of good quality.
In [MRSZ-06]
an heuristic stopping criterion based on the norm of the difference
of two successive solutions is introduced
for the truncation of the iteration of the bidiagonalization
Lanczos method in the computation of the regularized
solution of a least square problem.
Furthermore, it is shown how such criterion could be used for
determining a search interval of the corner for the L-curve.
A
parallel computing approach to dynamic
magnetic resonance imaging
Researchers.
F. Zama, E. Loli Piccolomini, G. Landi.
Advances.
In [LLZ-05]
a reconstruction algorithm for the RNM representing the
signal by means of the B-spline functions
is proposed. The algorithm requires to solve many ill-conditioned
subproblems of small size.
Between different regularization schemes, truncation criteria of
the conjugate gradient iteration are examined.
These criteria are based on the residual and solution norm.
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