86,987 research outputs found
SOCP relaxation bounds for the optimal subset selection problem applied to robust linear regression
This paper deals with the problem of finding the globally optimal subset of h
elements from a larger set of n elements in d space dimensions so as to
minimize a quadratic criterion, with an special emphasis on applications to
computing the Least Trimmed Squares Estimator (LTSE) for robust regression. The
computation of the LTSE is a challenging subset selection problem involving a
nonlinear program with continuous and binary variables, linked in a highly
nonlinear fashion. The selection of a globally optimal subset using the branch
and bound (BB) algorithm is limited to problems in very low dimension,
tipically d<5, as the complexity of the problem increases exponentially with d.
We introduce a bold pruning strategy in the BB algorithm that results in a
significant reduction in computing time, at the price of a negligeable accuracy
lost. The novelty of our algorithm is that the bounds at nodes of the BB tree
come from pseudo-convexifications derived using a linearization technique with
approximate bounds for the nonlinear terms. The approximate bounds are computed
solving an auxiliary semidefinite optimization problem. We show through a
computational study that our algorithm performs well in a wide set of the most
difficult instances of the LTSE problem.Comment: 12 pages, 3 figures, 2 table
Exact Gap Computation for Code Coverage Metrics in ISO-C
Test generation and test data selection are difficult tasks for model based
testing. Tests for a program can be meld to a test suite. A lot of research is
done to quantify the quality and improve a test suite. Code coverage metrics
estimate the quality of a test suite. This quality is fine, if the code
coverage value is high or 100%. Unfortunately it might be impossible to achieve
100% code coverage because of dead code for example. There is a gap between the
feasible and theoretical maximal possible code coverage value. Our review of
the research indicates, none of current research is concerned with exact gap
computation. This paper presents a framework to compute such gaps exactly in an
ISO-C compatible semantic and similar languages. We describe an efficient
approximation of the gap in all the other cases. Thus, a tester can decide if
more tests might be able or necessary to achieve better coverage.Comment: In Proceedings MBT 2012, arXiv:1202.582
Qutrit witness from the Grothendieck constant of order four
In this paper, we prove that , where denotes the
Grothendieck constant of order . To this end, we use a branch-and-bound
algorithm commonly used in the solution of NP-hard problems. It has recently
been proven that . Here we prove that ,
which has implications for device-independent witnessing dimensions greater
than two. Furthermore, the algorithm with some modifications may find
applications in various black-box quantum information tasks with large number
of inputs and outputs.Comment: 13 pages, 2 figure
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Primal-dual variable neighborhood search for the simple plant-location problem
Copyright @ 2007 INFORMSThe variable neighborhood search metaheuristic is applied to the primal simple plant-location problem and to a reduced dual obtained by exploiting the complementary slackness conditions. This leads to (i) heuristic resolution of (metric) instances with uniform fixed costs, up to n = 15,000 users, and m = n potential locations for facilities with an error not exceeding 0.04%; (ii) exact solution of such instances with up to m = n = 7,000; and (iii) exact solutions of instances with variable fixed costs and up to m = n = 15, 000.This work is supported by NSERC Grant 105574-02; NSERC Grant OGP205041; and partly by the Serbian Ministry of Science, Project 1583
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