40,657 research outputs found
Optimization with Sparsity-Inducing Penalties
Sparse estimation methods are aimed at using or obtaining parsimonious
representations of data or models. They were first dedicated to linear variable
selection but numerous extensions have now emerged such as structured sparsity
or kernel selection. It turns out that many of the related estimation problems
can be cast as convex optimization problems by regularizing the empirical risk
with appropriate non-smooth norms. The goal of this paper is to present from a
general perspective optimization tools and techniques dedicated to such
sparsity-inducing penalties. We cover proximal methods, block-coordinate
descent, reweighted -penalized techniques, working-set and homotopy
methods, as well as non-convex formulations and extensions, and provide an
extensive set of experiments to compare various algorithms from a computational
point of view
Neural Connectivity with Hidden Gaussian Graphical State-Model
The noninvasive procedures for neural connectivity are under questioning.
Theoretical models sustain that the electromagnetic field registered at
external sensors is elicited by currents at neural space. Nevertheless, what we
observe at the sensor space is a superposition of projected fields, from the
whole gray-matter. This is the reason for a major pitfall of noninvasive
Electrophysiology methods: distorted reconstruction of neural activity and its
connectivity or leakage. It has been proven that current methods produce
incorrect connectomes. Somewhat related to the incorrect connectivity
modelling, they disregard either Systems Theory and Bayesian Information
Theory. We introduce a new formalism that attains for it, Hidden Gaussian
Graphical State-Model (HIGGS). A neural Gaussian Graphical Model (GGM) hidden
by the observation equation of Magneto-encephalographic (MEEG) signals. HIGGS
is equivalent to a frequency domain Linear State Space Model (LSSM) but with
sparse connectivity prior. The mathematical contribution here is the theory for
high-dimensional and frequency-domain HIGGS solvers. We demonstrate that HIGGS
can attenuate the leakage effect in the most critical case: the distortion EEG
signal due to head volume conduction heterogeneities. Its application in EEG is
illustrated with retrieved connectivity patterns from human Steady State Visual
Evoked Potentials (SSVEP). We provide for the first time confirmatory evidence
for noninvasive procedures of neural connectivity: concurrent EEG and
Electrocorticography (ECoG) recordings on monkey. Open source packages are
freely available online, to reproduce the results presented in this paper and
to analyze external MEEG databases
A distributed accelerated gradient algorithm for distributed model predictive control of a hydro power valley
A distributed model predictive control (DMPC) approach based on distributed
optimization is applied to the power reference tracking problem of a hydro
power valley (HPV) system. The applied optimization algorithm is based on
accelerated gradient methods and achieves a convergence rate of O(1/k^2), where
k is the iteration number. Major challenges in the control of the HPV include a
nonlinear and large-scale model, nonsmoothness in the power-production
functions, and a globally coupled cost function that prevents distributed
schemes to be applied directly. We propose a linearization and approximation
approach that accommodates the proposed the DMPC framework and provides very
similar performance compared to a centralized solution in simulations. The
provided numerical studies also suggest that for the sparsely interconnected
system at hand, the distributed algorithm we propose is faster than a
centralized state-of-the-art solver such as CPLEX
An improved multi-parametric programming algorithm for flux balance analysis of metabolic networks
Flux balance analysis has proven an effective tool for analyzing metabolic
networks. In flux balance analysis, reaction rates and optimal pathways are
ascertained by solving a linear program, in which the growth rate is maximized
subject to mass-balance constraints. A variety of cell functions in response to
environmental stimuli can be quantified using flux balance analysis by
parameterizing the linear program with respect to extracellular conditions.
However, for most large, genome-scale metabolic networks of practical interest,
the resulting parametric problem has multiple and highly degenerate optimal
solutions, which are computationally challenging to handle. An improved
multi-parametric programming algorithm based on active-set methods is
introduced in this paper to overcome these computational difficulties.
Degeneracy and multiplicity are handled, respectively, by introducing
generalized inverses and auxiliary objective functions into the formulation of
the optimality conditions. These improvements are especially effective for
metabolic networks because their stoichiometry matrices are generally sparse;
thus, fast and efficient algorithms from sparse linear algebra can be leveraged
to compute generalized inverses and null-space bases. We illustrate the
application of our algorithm to flux balance analysis of metabolic networks by
studying a reduced metabolic model of Corynebacterium glutamicum and a
genome-scale model of Escherichia coli. We then demonstrate how the critical
regions resulting from these studies can be associated with optimal metabolic
modes and discuss the physical relevance of optimal pathways arising from
various auxiliary objective functions. Achieving more than five-fold
improvement in computational speed over existing multi-parametric programming
tools, the proposed algorithm proves promising in handling genome-scale
metabolic models.Comment: Accepted in J. Optim. Theory Appl. First draft was submitted on
August 4th, 201
A hierarchical time-splitting approach for solving finite-time optimal control problems
We present a hierarchical computation approach for solving finite-time
optimal control problems using operator splitting methods. The first split is
performed over the time index and leads to as many subproblems as the length of
the prediction horizon. Each subproblem is solved in parallel and further split
into three by separating the objective from the equality and inequality
constraints respectively, such that an analytic solution can be achieved for
each subproblem. The proposed solution approach leads to a nested decomposition
scheme, which is highly parallelizable. We present a numerical comparison with
standard state-of-the-art solvers, and provide analytic solutions to several
elements of the algorithm, which enhances its applicability in fast large-scale
applications
Development of Interactive Support Systems for Multiobjective Decision Analysis under Uncertainty
This paper presents interactive multiobjective decision analysis support systems, called MIDASS, which is a newly developed interactive computer program for strategic use of expected utility theory. Decision analysis based on expected utility hypothesis is an established prescriptive approach for supporting business decisions under uncertainty, which embodies an effective procedure for seeking the best choice among alternatives. It is usually difficult, however, for the decision maker (DM) to apply it for the strategic use in the realistic business situations. MIDASS provides an integrated interactive computer system for supporting multiobjective decision analysis under uncertainty, which assists to derive an acceptable business solution for DM with the construction of his/her expected multiattribute utility fuction (EMUF).expected multiobjective decision analysis, MIDASS, expected multiattribute utility function (EMUF), intelligent decision support systems (IDSS).
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