376,463 research outputs found
Sparsity-Aware Adaptive Algorithms Based on Alternating Optimization with Shrinkage
This letter proposes a novel sparsity-aware adaptive filtering scheme and
algorithms based on an alternating optimization strategy with shrinkage. The
proposed scheme employs a two-stage structure that consists of an alternating
optimization of a diagonally-structured matrix that speeds up the convergence
and an adaptive filter with a shrinkage function that forces the coefficients
with small magnitudes to zero. We devise alternating optimization least-mean
square (LMS) algorithms for the proposed scheme and analyze its mean-square
error. Simulations for a system identification application show that the
proposed scheme and algorithms outperform in convergence and tracking existing
sparsity-aware algorithms.Comment: 10 pages, 3 figures. IEEE Signal Processing Letters, 201
Transversality Conditions for Infinite Horizon Variational Problems on Time Scales
We consider problems of the calculus of variations on unbounded time scales.
We prove the validity of the Euler-Lagrange equation on time scales for
infinite horizon problems, and a new transversality condition.Comment: Submitted 6-October-2009; Accepted 19-March-2010 in revised form; for
publication in "Optimization Letters"
Scale-free Networks from Optimal Design
A large number of complex networks, both natural and artificial, share the
presence of highly heterogeneous, scale-free degree distributions. A few
mechanisms for the emergence of such patterns have been suggested, optimization
not being one of them. In this letter we present the first evidence for the
emergence of scaling (and smallworldness) in software architecture graphs from
a well-defined local optimization process. Although the rules that define the
strategies involved in software engineering should lead to a tree-like
structure, the final net is scale-free, perhaps reflecting the presence of
conflicting constraints unavoidable in a multidimensional optimization process.
The consequences for other complex networks are outlined.Comment: 6 pages, 2 figures. Submitted to Europhysics Letters. Additional
material is available at http://complex.upc.es/~sergi/software.ht
On global minimizers of quadratic functions with cubic regularization
In this paper, we analyze some theoretical properties of the problem of
minimizing a quadratic function with a cubic regularization term, arising in
many methods for unconstrained and constrained optimization that have been
proposed in the last years. First we show that, given any stationary point that
is not a global solution, it is possible to compute, in closed form, a new
point with a smaller objective function value. Then, we prove that a global
minimizer can be obtained by computing a finite number of stationary points.
Finally, we extend these results to the case where stationary conditions are
approximately satisfied, discussing some possible algorithmic applications.Comment: Optimization Letters (2018
Exact Solutions of Holonomic Quantum Computation
Holonomic quantum computation is analyzed from geometrical viewpoint. We
develop an optimization scheme in which an arbitrary unitary gate is
implemented with a small circle in a complex projective space. Exact solutions
for the Hadamard, CNOT and 2-qubit discrete Fourier transform gates are
explicitly constructed.Comment: 11 pages, re-organized to be more comprehensive, references added,
style file of Physics Letters A is neede
A General Backwards Calculus of Variations via Duality
We prove Euler-Lagrange and natural boundary necessary optimality conditions
for problems of the calculus of variations which are given by a composition of
nabla integrals on an arbitrary time scale. As an application, we get
optimality conditions for the product and the quotient of nabla variational
functionals.Comment: Submitted to Optimization Letters 03-June-2010; revised 01-July-2010;
accepted for publication 08-July-201
L1 Control Theoretic Smoothing Splines
In this paper, we propose control theoretic smoothing splines with L1
optimality for reducing the number of parameters that describes the fitted
curve as well as removing outlier data. A control theoretic spline is a
smoothing spline that is generated as an output of a given linear dynamical
system. Conventional design requires exactly the same number of base functions
as given data, and the result is not robust against outliers. To solve these
problems, we propose to use L1 optimality, that is, we use the L1 norm for the
regularization term and/or the empirical risk term. The optimization is
described by a convex optimization, which can be efficiently solved via a
numerical optimization software. A numerical example shows the effectiveness of
the proposed method.Comment: Accepted for publication in IEEE Signal Processing Letters. 4 pages
(twocolumn), 5 figure
Information content versus word length in random typing
Recently, it has been claimed that a linear relationship between a measure of
information content and word length is expected from word length optimization
and it has been shown that this linearity is supported by a strong correlation
between information content and word length in many languages (Piantadosi et
al. 2011, PNAS 108, 3825-3826). Here, we study in detail some connections
between this measure and standard information theory. The relationship between
the measure and word length is studied for the popular random typing process
where a text is constructed by pressing keys at random from a keyboard
containing letters and a space behaving as a word delimiter. Although this
random process does not optimize word lengths according to information content,
it exhibits a linear relationship between information content and word length.
The exact slope and intercept are presented for three major variants of the
random typing process. A strong correlation between information content and
word length can simply arise from the units making a word (e.g., letters) and
not necessarily from the interplay between a word and its context as proposed
by Piantadosi et al. In itself, the linear relation does not entail the results
of any optimization process
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