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1.
In this paper, approximate solutions of vector optimization problems are analyzed via a metrically consistent ε-efficient concept. Several properties of the ε-efficient set are studied. By scalarization, necessary and sufficient conditions for approximate solutions of convex and
nonconvex vector optimization problems are provided; a characterization is obtained via generalized Chebyshev norms, attaining
the same precision in the vector problem as in the scalarization.
This research was partially supported by the Ministerio de Educación y Ciencia (Spain), Project MTM2006-02629 and by the Consejería
de Educación de la Junta de Castilla y León (Spain), Project VA027B06. The authors are grateful to the anonymous referees
for helpful comments and suggestions. 相似文献
2.
In this paper, we study a general optimization problem without linear structure under a reflexive and transitive relation
on a nonempty set E, and characterize the existence of efficient points and the domination property for a subset of E through a generalization of the order-completeness condition introduced earlier. Afterwards, we study the abstract optimization
problem by using generalized continuity concepts and establish various existence results. As an application, we extend and
improve several existence results given in the literature for an optimization problem involving set-valued maps under vector
and set criteria.
The work of the first author was partially supported by CONICYT-Chile through FONDECYT 107-0689 and FONDAP-Matemáticas Aplicadas
II; whereas that of the second and third author were supported in part by Ministerio de Educación y Ciencia (Spain), project
MTM2006-02629 and by Junta de Castilla y León (Spain) Project VA027B06. 相似文献
3.
In this paper, we consider shifted tridiagonal matrices. We prove that the standard algorithm to compute the LU factorization
in this situation is mixed forward-backward stable and, therefore, componentwise forward stable. Moreover, we give a formula
to compute the corresponding condition number in O(n) flops.
This research has been partially supported by Dirección General de Investigación (Ministerio de Ciencia y Tecnología) of Spain
through grants BFM2003-06335-C03-02 and MTM2006-06671 as well as by the Postdoctoral Fellowship EX2004-0658 provided by Ministerio
de Educación y Ciencia of Spain. 相似文献
4.
We present a new second-order directional derivative and study its properties. Using this derivative and the parabolic second-order
derivative, we establish second-order necessary and sufficient optimality conditions for a general scalar optimization problem
by means of the asymptotic and parabolic second-order tangent sets to the feasible set. For the sufficient conditions, the
initial space must be finite dimensional. Then, these conditions are applied to a general vector optimization problem obtaining
second-order optimality conditions that generalize the differentiable case. For this aim, we introduce a scalarization, and
the relationships between the different types of solutions to the vector optimization problem and the scalarized problem are
studied.
This research was partially supported by the Ministerio de Educación y Ciencia (Spain), under projects MTM2006-02629 and Ingenio
Mathematica (i-MATH) CSD2006-00032 (Consolider-Ingenio 2010), and by the Consejería de Educación de la Junta de Castilla y
León (Spain), Project VA027B06.
The authors are grateful to the anonymous referees for valuable comments and suggestions. 相似文献
5.
Higgs bundles and non-abelian Hodge theory provide holomorphic methods with which to study the moduli spaces of surface group
representations in a reductive Lie group G. In this paper we survey the case in which G is the isometry group of a classical Hermitian symmetric space of non-compact type. Using Morse theory on the moduli spaces
of Higgs bundles, we compute the number of connected components of the moduli space of representations with maximal Toledo
invariant
Members of VBAC (Vector Bundles on Algebraic Curves). Second and Third authors partially supported by Ministerio de Educación
y Ciencia and Conselho de Reitores das Universidades Portuguesas through Acción Integrada Hispano-Lusa HP2002-0017 (Spain)/E–30/03
(Portugal). First and Second authors partially supported by Ministerio de Educación y Ciencia (Spain) through Project MTM2004-07090-C03-01.
Third author partially supported by the Centro de Matemática da Universidade do Porto and the project POCTI/MAT/58549/2004,
financed by FCT (Portugal) through the programmes POCTI and POSI of the QCA III (2000–2006) with European Community (FEDER)
and national funds. The second author visited the IHES with the partial support of the European Commission through its 6th
Framework Programme “Structuring the European Research Area” and the Contract No. RITA-CT-2004-505493 for the provision of
Transnational Access implemented as Specific Support Action 相似文献
6.
The approach to optimal control problems based on a purely variational reformulation may lead to new existence results by
using fine, general existence theorems for variational problems without convexity assumptions. We illustrate this perspective
here for autonomous one-dimensional problems and defer the study of more complex situations to later work.
This research was supported by Project MTM2004-07114 from Ministerio de Educación y Ciencia (Spain) and by Grant PAI05-029
from JCCM (Castilla-La Mancha). 相似文献
7.
Ignacio García-Jurado Natividad Llorca Ana Meca Manuel A. Pulido Joaquín Sánchez-Soriano 《TOP》2009,17(1):85-95
In this paper we consider finitely repeated games in which players can unilaterally commit to behave in an absentminded way
in some stages of the repeated game. We prove that the standard conditions for folk theorems can be substantially relaxed
when players are able to make this kind of compromises, both in the Nash and in the subgame perfect case. We also analyze
the relation of our model with the repeated games with unilateral commitments studied, for instance, in García-Jurado et al.
(Int. Game Theory Rev. 2:129–139, 2000).
Authors acknowledge the financial support of Ministerio de Educaci ón y Ciencia, FEDER and Fundación Séneca de la Región de Murcia through projects SEJ2005-07637-C02-02, ECO2008-03484-C02-02, MTM2005-09184-C02-02, MTM2008-06778-C02-01 and 08716/PI/08. 相似文献
8.
A practical implementation of the coherence function for evaluating the linear degree of a stochastic system is developed.
It is applied to several well known linear and nonlinear systems.
This paper has been partially supported by projects BFM2000-1466 and BFM2000-1103 from Plan Nacional de Investigación Científica,
Desarrollo e Innovación Tecnológico. Ministerio de Ciencia y Tecnología. Spain. The authors are grateful to the Associated
Editor and two anonymous referees whose comments and suggestions were helpful in improving the final version of this paper. 相似文献
9.
In this paper we establish characterization results for the continuous and discrete inf-sup conditions on product spaces.
The inf-sup condition for each component of the bilinear form involved and suitable decompositions of the pivot space in terms
of the associated null spaces are the key ingredients of our theorems. We illustrate the theory through its application to
bilinear forms arising from the variational formulations of several boundary value problems.
Dedicated to Professor Ivo Babuska on the occasion of his 82nd birthday.
This research was partially supported by Centro de Modelamiento Matemático (CMM) of the Universidad de Chile, by Centro de
Investigación en Ingenierí a Matemática (CI2MA) of the Universidad de Concepción, by FEDER/MCYT Project MTM2007-63204, and by Gobierno de Aragón (Grupo Consolidado PDIE). 相似文献
10.
Antonio J. Ureña 《Archiv der Mathematik》2008,91(1):63-75
We consider the periodic action functional associated to some Lagrangian verifying the Legendre convexity condition and show
that all minimizers are unstable.
Supported by D.G.I. MTM2005-03483, Ministerio de Educación y Ciencia, Spain. 相似文献
11.
Extending the Levy-Steinitz rearrangement theorem in ℝ
n
, which in turn extended Riemann’s theorem, Banaszczyk proved in 1990/93 that a metrizable, locally convex space is nuclear
if and only if the domain of sums of every convergent series (i.e. the set of all elements in the space which are sums of
a convergent rearrangement of the series) is a translate of a closed subspace of a special form. In this paper we present
an apparently complete analysis of the domains of sums of convergent series in duals of metrizable spaces or, more generally,
in (DF)-spaces in the sense of Grothendieck.
The research of the first author was partially supported by DGES Project PB97-0333, and the second one by a grant of the Ministerio
de Educatión y Cultura of Spain (Ref: Sab 1995-0736). 相似文献
12.
R. Josa-Fombellida J. P. Rincón-Zapatero 《Journal of Optimization Theory and Applications》2007,135(1):163-177
This paper provides new insights into the solution of optimal stochastic control problems by means of a system of partial
differential equations, which characterize directly the optimal control. This new system is obtained by the application of
the stochastic maximum principle at every initial condition, assuming that the optimal controls are smooth enough. The type
of problems considered are those where the diffusion coefficient is independent of the control variables, which are supposed
to be interior to the control region.
Two referees provided useful suggestions. Both authors gratefully acknowledge financial support from the regional Government
of Castilla y León (Spain) under Project VA099/04, the Spanish Ministry of Education and Science and FEDER funds under Project
MTM2005-06534. 相似文献
13.
The Nevalinna–Pick algorithm yields a continued fraction expansion of every Schur function, whose approximants are identified.
These approximants are quotients of rational functions which can be understood as the rational analogs of the Wall polynomials.
The properties of these Wall rational functions and the corresponding approximants permit us to obtain a Khrushchev’s formula
for orthogonal rational functions. An introduction to the convergence of the Wall approximants in the indeterminate case is
presented.
This work was partially realized during two stays of the second author at the Norwegian University of Science and Technology
(NTNU) financed respectively by Secretaría de Estado de Universidades e Investigación from the Ministry of Education and Science
of Spain and by the Department of Mathematical Sciences of NTNU. The work of the second author was also partially supported
by the Spanish grants from the Ministry of Education and Science, project code MTM2005-08648-C02-01, and the Ministry of Science
and Innovation, project code MTM2008-06689-C02-01, and by Project E-64 of Diputación General de Aragón (Spain). 相似文献
14.
In this paper we study the influence of the partial cover and avoidance property on the subgroups of some relevant families of subgroups in a finite group. 相似文献
15.
O. Blasco M. D. Contreras S. Díaz-Madrigal J. Martínez A. G. Siskakis 《Integral Equations and Operator Theory》2008,61(1):45-62
In this paper we deal with the maximal subspace in BMOA where a general semigroup of analytic functions on the unit disk generates a strongly continuous semigroup of composition
operators. Particular cases of this question are related to a well-known theorem of Sarason about VMOA. Our results describe analytically that maximal subspace and provide a condition which is sufficient for the maximal subspace
to be exactly VMOA. A related necessary condition is also proved in the case when the semigroup has an inner Denjoy-Wolff point. As a byproduct
we provide a generalization of the theorem of Sarason.
This research has been partially supported by the Ministerio de Educación y Ciencia projects n. MTM2006-14449-C02-01 and MTM2005-08350-C03-03 and by La Consejería de Educación y Ciencia de la Junta de Andalucía. 相似文献
16.
Gabriel N. Gatica Antonio Márquez Salim Meddahi 《Advances in Computational Mathematics》2009,30(3):281-301
This paper deals with the scattering of time harmonic electromagnetic waves by an infinitely long cylinder containing a non-homogeneous
conducting medium. More precisely, we study the transverse magnetic field that solves an interface problem holding between
the cross section of the cylinder and the exterior two-dimensional free space. We apply a dual-mixed variational formulation
in the obstacle coupled with a boundary integral equation method in the unbounded homogeneous space. A Fredholm alternative
is utilized to prove that this continuous formulation is well posed. We define the corresponding discrete scheme by using
the lowest order rotated Raviart-Thomas finite elements for the magnetic field and spectral elements for the boundary unknown.
Then, we show that the resulting Galerkin scheme is uniquely solvable and convergent, and prove optimal error estimates. Finally,
we illustrate our analysis with some results from computational experiments.
This research was partially supported by CONICYT-Chile through the FONDAP Program in Applied Mathematics, by the Dirección
de Investigación of the Universidad de Concepción through the Advanced Research Groups Program, and by the Ministerio de Educación
y Ciencia of Spain, through the project No. MTM2004-05417. 相似文献
17.
M. A. Mosquera I. García-Jurado M. G. Fiestras-Janeiro 《Annals of Operations Research》2008,158(1):183-188
In this note we deal with inventory games as defined in Meca et al. (Math. Methods Oper. Res. 57:483–491, 2003). In that context we introduce the property of immunity to coalitional manipulation, and demonstrate that the SOC-rule (Share the Ordering Cost) is the unique allocation rule for inventory games which satisfies
this property.
The authors acknowledge the financial support of Ministerio de Educación y Ciencia, FEDER and Xunta de Galicia through projects SEJ2005-07637-C02-02 and PGIDIT06PXIC207038PN. 相似文献
18.
Computing estimates in functional principal component analysis (FPCA) from discrete data is usually based on the approximation
of sample curves in terms of a basis (splines, wavelets, trigonometric functions, etc.) and a geometrical structure in the
data space (L
2 spaces, Sobolev spaces, etc.). Until now, the computational efforts have been focused in developing ad hoc algorithms to
approximate those estimates by previously selecting an efficient approximating technique and a convenient geometrical structure.
The main goal of this paper consists of establishing a procedure to formulate the algorithm for computing estimates of FPCA
under general settings. The resulting algorithm is based on the classic multivariate PCA of a certain random vector and can
thus be implemented in the majority of statistical packages. In fact, it is derived from the analysis of the effects of modifying
the norm in the space of coordinates. Finally, an application on real data will be developed to illustrate the so derived
theoretic results.
This research has been supported by Project MTM2004-5992 from Dirección General de Investigación, Ministerio de Ciencia y
Tecnología. 相似文献
19.
In this paper we prove that theories obtained via a cone or an arc object in additive categories are homotopy theories of
Δ-abelian groups.
Research supported in path by the Consejería de Educación de Canarias, (Project n. 11/02.06.87 and Project n. 48/01.06.88)
and the ONCE. 相似文献
20.
Miguel Sama 《Set-Valued and Variational Analysis》2009,17(1):41-61
A theory of second order differentiability for real functions with calm Clarke gradient at points of strict differentiability
is presented from a set-valued analysis perspective by using the theory of graphical derivatives of set-valued maps. Connections
with other second order theories and applications in optimization are given.
This work is partially supported by Ministerio de Educación y Ciencia (Spain), project MTM2006-02629 and IngenioMathematica
(i-MATH) CSD2006-00032 (Consolider-Ingenio 2010). 相似文献