Seminário temático
de IO – Otimização, CMA-FCT-UNL
Data e hora:
Terça-feira, 07 de junho, 14h00 – 16h30
Local: Sala 1.17,
Edifício VII, FCT-UNL
Título, orador
(afiliação), resumo:
1)
Separable cubic modeling with impact in global optimization, Marcos Raydan (Simon Bolivar University, Caracas,
Venezuela)
A separable cubic
model, for smooth unconstrained minimization, is proposed and
evaluated. The cubic model uses some novel secant-type choices
for the parameters in the cubic terms. A suitable hard-case-free
trust-region strategy that takes advantage of the separable
cubic modeling is also presented. Some numerical examples are
presented to illustrate the tendency of the specialized
trust-region algorithm, when combined with our cubic modeling,
to escape from local minimizers. For large-scale problems, we
analyze a specialized strategy to minimize the cubic model on a
properly chosen low-dimensional subspace, which is built at each
iteration using the Lanczos process. For the convergence
analysis we establish asymptotic as well as complexity
convergence results to second-order stationary points.
2) Spectral
simplex gradient method for unconstrained optimization,
Milagros Loreto (University of Washington Bothell, USA)
To solve nonsmooth
unconstrained minimization problems, we combine the spectral
choice of step length with the simplex gradient method. The
simplex gradient method is a direct search method that only
requires function evaluations to build an approximation to the
gradient direction. The spectral step is related to the
quasi-Newton family of methods through an approximated secant
equation, requires little computational work and can be easily
adapted to different optimization scenarios. The proposed
spectral simplex gradient method (SpecSimplex) includes a
suitable non-monotone line search strategy. To illustrate the
behavior of SpecSimplex, we present and discuss encouraging
numerical results on a set of nonsmooth test functions.
3) Surfaces of
minimal energy. Applications, Miguel Ángel Fortes
(University of Granada, Spain)
In the last years, a
wide range of variational methods have received considerable
attention in CAGD, due to their efficiency and usefulness in
the field of surface design. The basic idea of these methods is
to minimize, in an appropriate functional space, a functional
derived from geometric considerations (data fitting, surface
area, curvature, shape or volume preserving,...)
These functionals typically contain two terms: one fi tting a
Lagrangian given data-set, and another one which controls the
smoothness and the geometric constraints of the desired
surfaces. Both summands are a ffected by weights in order to
give more importance to one aspect than to another ones.
In this seminar, we show some of the results obtained in this
fi eld:
°
Obtention of C1-spline
surfaces of minimal energy of total degree two fitting
Lagrangian data-sets
°
Multiresolution analysis: we have developed some algorithms
which allow us to obtain minimal energy surfaces at di fferent
resolution levels. As an application, we have design techniques
to reduce the noise of a given surface as well as to localize
the regions of maximum energy of a given function.
°
The "hole filling problem", i. e., the problem of finding
"patches" fi lling the holes of a given surface. By using the
technique of functional energy minimization, we have described
di fferent solutions to this problem.
Finally, several open problems regarding this researching line
will be exposed.