137,950 research outputs found
The linearization problem of a binary quadratic problem and its applications
We provide several applications of the linearization problem of a binary
quadratic problem. We propose a new lower bounding strategy, called the
linearization-based scheme, that is based on a simple certificate for a
quadratic function to be non-negative on the feasible set. Each
linearization-based bound requires a set of linearizable matrices as an input.
We prove that the Generalized Gilmore-Lawler bounding scheme for binary
quadratic problems provides linearization-based bounds. Moreover, we show that
the bound obtained from the first level reformulation linearization technique
is also a type of linearization-based bound, which enables us to provide a
comparison among mentioned bounds. However, the strongest linearization-based
bound is the one that uses the full characterization of the set of linearizable
matrices. Finally, we present a polynomial-time algorithm for the linearization
problem of the quadratic shortest path problem on directed acyclic graphs. Our
algorithm gives a complete characterization of the set of linearizable matrices
for the quadratic shortest path problem
Linearization of analytic and non--analytic germs of diffeomorphisms of
We study Siegel's center problem on the linearization of germs of
diffeomorphisms in one variable. In addition of the classical problems of
formal and analytic linearization, we give sufficient conditions for the
linearization to belong to some algebras of ultradifferentiable germs closed
under composition and derivation, including Gevrey classes.
In the analytic case we give a positive answer to a question of J.-C. Yoccoz
on the optimality of the estimates obtained by the classical majorant series
method.
In the ultradifferentiable case we prove that the Brjuno condition is
sufficient for the linearization to belong to the same class of the germ. If
one allows the linearization to be less regular than the germ one finds new
arithmetical conditions, weaker than the Brjuno condition. We briefly discuss
the optimality of our results.Comment: AMS-Latex2e, 11 pages, in press Bulletin Societe Mathematique de
Franc
Optimality of nonlinear design techniques: A converse HJB approach
The issue of optimality in nonlinear controller design is confronted by using the converse HJB approach to classify dynamics under which certain design schemes are optimal. In particular, the techniques of Jacobian linearization, pseudo-Jacobian linearization, and feedback linearization are analyzed. Finally, the conditions for optimality are applied to the 2-D nonlinear oscillator, where simple, nontrivial examples are produced in which the various design techniques are optimal
Linearization of CIF Through SOS
Linearization is the procedure of rewriting a process term into a linear
form, which consist only of basic operators of the process language. This
procedure is interesting both from a theoretical and a practical point of view.
In particular, a linearization algorithm is needed for the Compositional
Interchange Format (CIF), an automaton based modeling language.
The problem of devising efficient linearization algorithms is not trivial,
and has been already addressed in literature. However, the linearization
algorithms obtained are the result of an inventive process, and the proof of
correctness comes as an afterthought. Furthermore, the semantic specification
of the language does not play an important role on the design of the algorithm.
In this work we present a method for obtaining an efficient linearization
algorithm, through a step-wise refinement of the SOS rules of CIF. As a result,
we show how the semantic specification of the language can guide the
implementation of such a procedure, yielding a simple proof of correctness.Comment: In Proceedings EXPRESS 2011, arXiv:1108.407
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