132 research outputs found
A two-phase gradient method for quadratic programming problems with a single linear constraint and bounds on the variables
We propose a gradient-based method for quadratic programming problems with a
single linear constraint and bounds on the variables. Inspired by the GPCG
algorithm for bound-constrained convex quadratic programming [J.J. Mor\'e and
G. Toraldo, SIAM J. Optim. 1, 1991], our approach alternates between two phases
until convergence: an identification phase, which performs gradient projection
iterations until either a candidate active set is identified or no reasonable
progress is made, and an unconstrained minimization phase, which reduces the
objective function in a suitable space defined by the identification phase, by
applying either the conjugate gradient method or a recently proposed spectral
gradient method. However, the algorithm differs from GPCG not only because it
deals with a more general class of problems, but mainly for the way it stops
the minimization phase. This is based on a comparison between a measure of
optimality in the reduced space and a measure of bindingness of the variables
that are on the bounds, defined by extending the concept of proportioning,
which was proposed by some authors for box-constrained problems. If the
objective function is bounded, the algorithm converges to a stationary point
thanks to a suitable application of the gradient projection method in the
identification phase. For strictly convex problems, the algorithm converges to
the optimal solution in a finite number of steps even in case of degeneracy.
Extensive numerical experiments show the effectiveness of the proposed
approach.Comment: 30 pages, 17 figure
Constraint-Preconditioned Krylov Solvers for Regularized Saddle-Point Systems
We consider the iterative solution of regularized saddle-point systems. When
the leading block is symmetric and positive semi-definite on an appropriate
subspace, Dollar, Gould, Schilders, and Wathen (2006) describe how to apply the
conjugate gradient (CG) method coupled with a constraint preconditioner, a
choice that has proved to be effective in optimization applications. We
investigate the design of constraint-preconditioned variants of other Krylov
methods for regularized systems by focusing on the underlying basis-generation
process. We build upon principles laid out by Gould, Orban, and Rees (2014) to
provide general guidelines that allow us to specialize any Krylov method to
regularized saddle-point systems. In particular, we obtain
constraint-preconditioned variants of Lanczos and Arnoldi-based methods,
including the Lanczos version of CG, MINRES, SYMMLQ, GMRES(m) and DQGMRES. We
also provide MATLAB implementations in hopes that they are useful as a basis
for the development of more sophisticated software. Finally, we illustrate the
numerical behavior of constraint-preconditioned Krylov solvers using symmetric
and nonsymmetric systems arising from constrained optimization.Comment: Accepted for publication in the SIAM Journal on Scientific Computin
Affect Recognition in Autism: a single case study on integrating a humanoid robot in a standard therapy.
Autism Spectrum Disorder (ASD) is a multifaceted developmental disorder that comprises a mixture of social impairments, with deficits in many areas including the theory of mind, imitation, and communication. Moreover, people with autism have difficulty in recognising and understanding emotional expressions. We are currently working on integrating a humanoid robot within the standard clinical treatment offered to children with ASD to support the therapists. In this article, using the A-B-A' single case design, we propose a robot-assisted affect recognition training and to present the results on the child’s progress during the five months of clinical experimentation. In the investigation, we tested the generalization of learning and the long-term maintenance of new skills via the NEPSY-II affection recognition sub-test. The results of this single case study suggest the feasibility and effectiveness of using a humanoid robot to assist with emotion recognition training in children with ASD
Directional TGV-based image restoration under Poisson noise
We are interested in the restoration of noisy and blurry images where the
texture mainly follows a single direction (i.e., directional images). Problems
of this type arise, for example, in microscopy or computed tomography for
carbon or glass fibres. In order to deal with these problems, the Directional
Total Generalized Variation (DTGV) was developed by Kongskov et al. in 2017 and
2019, in the case of impulse and Gaussian noise. In this article we focus on
images corrupted by Poisson noise, extending the DTGV regularization to image
restoration models where the data fitting term is the generalized
Kullback-Leibler divergence. We also propose a technique for the identification
of the main texture direction, which improves upon the techniques used in the
aforementioned work about DTGV. We solve the problem by an ADMM algorithm with
proven convergence and subproblems that can be solved exactly at a low
computational cost. Numerical results on both phantom and real images
demonstrate the effectiveness of our approach.Comment: 20 pages, 1 table, 13 figure
Using gradient directions to get global convergence of Newton-type methods
The renewed interest in Steepest Descent (SD) methods following the work of
Barzilai and Borwein [IMA Journal of Numerical Analysis, 8 (1988)] has driven
us to consider a globalization strategy based on SD, which is applicable to any
line-search method. In particular, we combine Newton-type directions with
scaled SD steps to have suitable descent directions. Scaling the SD directions
with a suitable step length makes a significant difference with respect to
similar globalization approaches, in terms of both theoretical features and
computational behavior. We apply our strategy to Newton's method and the BFGS
method, with computational results that appear interesting compared with the
results of well-established globalization strategies devised ad hoc for those
methods.Comment: 22 pages, 11 Figure
ACQUIRE: an inexact iteratively reweighted norm approach for TV-based Poisson image restoration
We propose a method, called ACQUIRE, for the solution of constrained
optimization problems modeling the restoration of images corrupted by Poisson
noise. The objective function is the sum of a generalized Kullback-Leibler
divergence term and a TV regularizer, subject to nonnegativity and possibly
other constraints, such as flux conservation. ACQUIRE is a line-search method
that considers a smoothed version of TV, based on a Huber-like function, and
computes the search directions by minimizing quadratic approximations of the
problem, built by exploiting some second-order information. A classical
second-order Taylor approximation is used for the Kullback-Leibler term and an
iteratively reweighted norm approach for the smoothed TV term. We prove that
the sequence generated by the method has a subsequence converging to a
minimizer of the smoothed problem and any limit point is a minimizer.
Furthermore, if the problem is strictly convex, the whole sequence is
convergent. We note that convergence is achieved without requiring the exact
minimization of the quadratic subproblems; low accuracy in this minimization
can be used in practice, as shown by numerical results. Experiments on
reference test problems show that our method is competitive with
well-established methods for TV-based Poisson image restoration, in terms of
both computational efficiency and image quality.Comment: 37 pages, 13 figure
Spatially Adaptive Regularization in Image Segmentation
We modify the total-variation-regularized image segmentation model proposed
by Chan, Esedoglu and Nikolova [SIAM Journal on Applied Mathematics 66, 2006]
by introducing local regularization that takes into account spatial image
information. We propose some techniques for defining local regularization
parameters, based on the cartoon-texture decomposition of the given image, on
the mean and median filters, and on a thresholding technique, with the aim of
preventing excessive regularization in piecewise-constant or smooth regions and
preserving spatial features in nonsmooth regions. We solve the modified model
by using split Bregman iterations. Numerical experiments show the effectiveness
of our approach
Deep learning systems for estimating visual attention in robot-assisted therapy of children with autism and intellectual disability
Recent studies suggest that some children with autism prefer robots as tutors for improving their social interaction and communication abilities which are impaired due to their disorder. Indeed, research has focused on developing a very promising form of intervention named Robot-Assisted Therapy. This area of intervention poses many challenges, including the necessary flexibility and adaptability to real unconstrained therapeutic settings, which are different from the constrained lab settings where most of the technology is typically tested. Among the most common impairments of children with autism and intellectual disability is social attention, which includes difficulties in establishing the correct visual focus of attention. This article presents an investigation on the use of novel deep learning neural network architectures for automatically estimating if the child is focusing their visual attention on the robot during a therapy session, which is an indicator of their engagement. To study the application, the authors gathered data from a clinical experiment in an unconstrained setting, which provided low-resolution videos recorded by the robot camera during the child–robot interaction. Two deep learning approaches are implemented in several variants and compared with a standard algorithm for face detection to verify the feasibility of estimating the status of the child directly from the robot sensors without relying on bulky external settings, which can distress the child with autism. One of the proposed approaches demonstrated a very high accuracy and it can be used for off-line continuous assessment during the therapy or for autonomously adapting the intervention in future robots with better computational capabilities
Adapting robot-assisted therapy of children with autism and different levels of intellectual disability
Autism Spectrum Disorder (ASD) is a complex developmental disorder that requires personalising the treatment to the personal condition, in particular for individuals with Intellectual Disability (ID), which are the majority of those with ASD.
In this paper, we present a preliminary analysis of our on-going research on personalised care for children with ASD and ID. The investigation focuses on integrating a social robot within the standard treatment in which tasks and level of interaction are adapted to the ID level of the individual and follow his progress after the rehabilitation
LSOS: Line-search Second-Order Stochastic optimization methods for nonconvex finite sums
We develop a line-search second-order algorithmic framework for minimizing
finite sums. We do not make any convexity assumptions, but require the terms of
the sum to be continuously differentiable and have Lipschitz-continuous
gradients. The methods fitting into this framework combine line searches and
suitably decaying step lengths. A key issue is a two-step sampling at each
iteration, which allows us to control the error present in the line-search
procedure. Stationarity of limit points is proved in the almost-sure sense,
while almost-sure convergence of the sequence of approximations to the solution
holds with the additional hypothesis that the functions are strongly convex.
Numerical experiments, including comparisons with state-of-the art stochastic
optimization methods, show the efficiency of our approach.Comment: 22 pages, 4 figure
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