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1.
In this paper we consider the general cone programming problem, and propose primal-dual convex (smooth and/or nonsmooth) minimization
reformulations for it. We then discuss first-order methods suitable for solving these reformulations, namely, Nesterov’s optimal
method (Nesterov in Doklady AN SSSR 269:543–547, 1983; Math Program 103:127–152, 2005), Nesterov’s smooth approximation scheme
(Nesterov in Math Program 103:127–152, 2005), and Nemirovski’s prox-method (Nemirovski in SIAM J Opt 15:229–251, 2005), and
propose a variant of Nesterov’s optimal method which has outperformed the latter one in our computational experiments. We
also derive iteration-complexity bounds for these first-order methods applied to the proposed primal-dual reformulations of
the cone programming problem. The performance of these methods is then compared using a set of randomly generated linear programming
and semidefinite programming instances. We also compare the approach based on the variant of Nesterov’s optimal method with
the low-rank method proposed by Burer and Monteiro (Math Program Ser B 95:329–357, 2003; Math Program 103:427–444, 2005) for
solving a set of randomly generated SDP instances. 相似文献
2.
Gia Sirbiladze 《Fuzzy Optimization and Decision Making》2010,9(3):233-274
This work deals with the problems of the Continuous Extremal Fuzzy Dynamic System (CEFDS) optimization and briefly discusses
the results developed by Sirbiladze (Int J Gen Syst 34(2):107–138, 2005a; 34(2):139–167, 2005b; 34(2):169–198, 2005c; 35(4):435–459,
2006a; 35(5):529–554, 2006b; 36(1): 19–58, 2007; New Math Nat Comput 4(1):41–60, 2008a; Mat Zametki, 83(3):439–460, 2008b).
The basic properties of extended extremal fuzzy measures and Sugeno’s type integrals are considered and several variants of
their representation are given. Values of extended extremal conditional fuzzy measures are defined as a levels of expert knowledge
reflections of CEFDS states in the fuzzy time intervals. The notions of extremal fuzzy time moments and intervals are introduced
and their monotone algebraic structures that form the most important part of the fuzzy instrument of modeling extremal fuzzy
dynamic systems are discussed. A new approach in modeling of CEFDS is developed. Applying the results of Sirbiladze (Int J
Gen Syst 34(2) 107–138, 2005a; 34(2):139–167, 2005b), fuzzy processes with possibilistic uncertainty, the source of which
are expert knowledge reflections on the states on CEFDS in extremal fuzzy time intervals, are constructed (Sirbiladze in Int
J Gen Syst 34(2):169–198, 2005c). The dynamics of CEFDS’s is described. Questions of the ergodicity of CEFDS are considered.
A fuzzy-integral representation of a continuous extremal fuzzy process is given. Based on the fuzzy-integral model, a method
and an algorithm are developed for identifying the transition operator of CEFDS. The CEFDS transition operator is restored
by means of expert data with possibilistic uncertainty, the source of which is expert knowledge reflections on the states
of CEFDS in the extremal fuzzy time intervals. The regularization condition for obtaining quasi-optimal estimator of the transition
operator is represented by the theorems. The corresponding calculating algorithm is provided. The results obtained are illustrated
by an example in the case of a finite set of CEFDS states. 相似文献
3.
Alicia Cordero José L. Hueso Eulalia Martínez Juan R. Torregrosa 《Numerical Algorithms》2010,53(4):485-495
In this paper, we present two new three-step iterative methods for solving nonlinear equations with sixth convergence order.
The new methods are obtained by composing known methods of third order of convergence with Newton’s method and using an adequate
approximation for the derivative, that provides high order of convergence and reduces the required number of functional evaluations
per step. The first method is obtained from Potra-Pták’s method and the second one, from Homeier’s method, both reaching an
efficiency index of 1.5651. Our methods are comparable with the method of Parhi and Gupta (Appl Math Comput 203:50–55, 2008). Methods proposed by Kou and Li (Appl Math Comput 189:1816–1821, 2007), Wang et al. (Appl Math Comput 204:14–19, 2008) and Chun (Appl Math Comput 190:1432–1437, 2007) reach the same efficiency index, although they start from a fourth order method while we use third order methods and simpler
arithmetics. We prove the convergence results and check them with several numerical tests that allow us to compare the convergence
order, the computational cost and the efficiency order of our methods with those of the original methods. 相似文献
4.
V. A. Zalgaller 《Journal of Mathematical Sciences》2007,140(4):511-527
It is proved that a regular tetrahedron has the maximal possible surface area among all tetrahedra having surface with unit
geodesic diameter. An independent proof of O’Rourke-Schevon’s theorem about polar points on a convex polyhedron is given.
A. D. Aleksandrov’s general problem on the area of a convex surface with fixed geodesic diameter is discussed. Bibliography:
4 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 329, 2005, pp. 28–55. 相似文献
5.
We consider the problem of Adverse Selection and optimal derivative design within a Principal–Agent framework. The principal’s
income is exposed to non-hedgeable risk factors arising, for instance, from weather or climate phenomena. She evaluates her
risk using a coherent and law invariant risk measure and tries minimize her exposure by selling derivative securities on her
income to individual agents. The agents have mean–variance preferences with heterogeneous risk aversion coefficients. An agent’s
degree of risk aversion is private information and hidden from the principal who only knows the overall distribution. We show
that the principal’s risk minimization problem has a solution and illustrate the effects of risk transfer on her income by
means of two specific examples. Our model extends earlier work of Barrieu and El Karoui (in Financ Stochast 9, 269–298, 2005)
and Carlier et al. (in Math Financ Econ 1, 57–80, 2007).
We thank Guillaume Carlier, Pierre-Andre Chiappori, Ivar Ekeland, Andreas Putz and seminar participants at various institutions
for valuable comments and suggestions. Financial support through an NSERC individual discovery grant is gratefully acknowledged. 相似文献
6.
In this paper, with the help of convex-like function, we discuss the duality theory for nonconvex semidefinite programming.
Our contributions are: duality theory for the general nonconvex semidefinite programming when Slater’s condition holds; perfect
duality for a special case of the nonconvex semidefinite programming for which Slater’s condition fails. We point out that
the results of Fan (Appl. Math. Lett. 18:1068–1073, 2005) can be regarded as a special case of our result. 相似文献
7.
In this paper we examine two classes of correlated aggregate claims distributions, with univariate claim counts and multivariate claim sizes. Firstly, we extend the results of Hesselager [ASTIN Bulletin, 24: 19-32(1994)] and Wang & Sobrero's [ASTIN Bulletin, 24:161-166 (1994)] concerning recursions for compound distributions to a multivariate situation where each claim event generates a random vector. Then we give a multivariate continuous version of recursive algorithm for calculating a family of compound distribution. Especially, to some extent, we obtain a continuous version of the corresponding results in Sundt [ASTIN Bulletin, 29:29-45 (1999)] and Ambagaspitiya [Insurance: Mathematics and Economics, 24:301-308 (1999)]. Finally, we give an example and show how to use the algorithm for aggregate claim distribution of first class to compute recursively the compound distribution. 相似文献
8.
We describe an algebro-geometric approach to Vakil–Zinger’s desingularization of the main component of the moduli of genus
one stable maps to
\mathbbPn{\mathbb{P}^{n}} (Vakil and Zinger in Res Announc Am Math Soc 13:53–59, 2007; Geom Topol 12(1):1–95, 2008). Our approach is based on understanding
the local structure of this moduli space; it also gives a partial desingularization of the entire moduli space. The results
proved should extend to higher genera. 相似文献
9.
Adam Bobrowski 《Journal of Evolution Equations》2010,10(3):663-675
We show that generation theorems for cosine families related to one-dimensional Laplacians in C[0, ∞] may be obtained by Lord Kelvin’s method of images, linking them with existence of invariant subspaces of the basic
cosine family. This allows us to deal with boundary conditions more general than those considered before (Bátkal and Engel
in J Differ Equ 207:1–20, 2004; Chill et al. in Functional analysis and evolution equations. The Günter Lumer volume, Birkhauser,
Basel, pp 113–130, 2007; Xiao and Liang in J Funct Anal 254:1467–1486, 2008) and to give explicit formulae for transition
kernels of related Brownian motions on [0, ∞). As another application we exhibit an example of a family of equibounded cosine
operator functions in C[0, ∞] that converge merely on C
0(0, ∞] while the corresponding semigroups converge on the whole of C[0, ∞]. 相似文献
10.
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
11.
Gabriela Jeronimo Guillermo Matera Pablo Solernó Ariel Waissbein 《Foundations of Computational Mathematics》2009,9(1):1-50
We exhibit a probabilistic symbolic algorithm for solving zero-dimensional sparse systems. Our algorithm combines a symbolic
homotopy procedure, based on a flat deformation of a certain morphism of affine varieties, with the polyhedral deformation
of Huber and Sturmfels. The complexity of our algorithm is cubic in the size of the combinatorial structure of the input system.
This size is mainly represented by the cardinality and mixed volume of Newton polytopes of the input polynomials and an arithmetic
analogue of the mixed volume associated to the deformations under consideration.
Research was partially supported by the following grants: UBACyT X112 (2004–2007), UBACyT X847 (2006–2009), PIP CONICET 2461,
PIP CONICET 5852/05, ANPCyT PICT 2005 17-33018, UNGS 30/3005, MTM2004-01167 (2004–2007), MTM2007-62799 and CIC 2007–2008. 相似文献
12.
A. G. Nikitin 《Ukrainian Mathematical Journal》2007,59(3):439-458
We complete the group classification of systems of two coupled nonlinear reaction-diffusion equations with general diffusion
matrix begun in author’s previous works. Namely, all nonequivalent equations with triangular diffusion matrix are classified.
In addition, we describe symmetries of diffusion systems with nilpotent diffusion matrix and additional terms with first-order
derivatives.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 3, pp. 395–411, March, 2007. 相似文献
13.
S. I. Kalmykov 《Journal of Mathematical Sciences》2009,157(4):623-631
The paper considers the equality cases in the rnajoration principle for meromorphic functions established earlier by V. N.
Dubinin and S. I. Kalmykov [Mat. Sb., 198, No. 12, 37–46 (2007)]. As corollaries of this principle, new inequalities for the coefficients and derivatives of polynomials
satisfying certain conditions on two intervals are obtained. Simple proofs of some Lukashov’s theorems on the derivatives
of rational functions on several intervals are provided. Bibliography: 13 titles.
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 357, 2008, pp. 143–157. 相似文献
14.
Thomas Mikosch 《Extremes》2006,9(1):3-20
“But he does not wear any clothes” said the little child in Hans Christian Andersen’s “The Emperor’s New Clothes.”Mikosch’s research is partially supported by the Danish Research Council (SNF) GrantNo 21-04-0400. This is a discussion paper which was initiated at the 4th InternationalConference on Extreme Value Analysis in Gothenburg, 15–19 August, 2005; see. 相似文献
15.
Hassan Oukhaba 《Mathematische Annalen》2006,336(3):639-657
In the first part of this paper we give a new definition of the elliptic analogue of Sinnott’s group of circular units. In this we essentially use the ideas discussed in Oukhaba (in Ann Inst Fourier, 55(33):753–772, 2005). In the second part of the paper we are interested in computing the index of this group of elliptic units. This question is closely related to the behaviour of the universal signed ordinary distributions introduced in loc. cit. Such distributions have a natural resolution discovered by Anderson. Consequently, we can apply Ouyang’s general index formula and the powerful Anderson’s theory of double complex to make the computations 相似文献
16.
We consider a generalized equilibrium problem involving DC functions which is called (GEP). For this problem we establish
two new dual formulations based on Toland-Fenchel-Lagrange duality for DC programming problems. The first one allows us to
obtain a unified dual analysis for many interesting problems. So, this dual coincides with the dual problem proposed by Martinez-Legaz
and Sosa (J Glob Optim 25:311–319, 2006) for equilibrium problems in the sense of Blum and Oettli. Furthermore it is equivalent
to Mosco’s dual problem (Mosco in J Math Anal Appl 40:202–206, 1972) when applied to a variational inequality problem. The
second dual problem generalizes to our problem another dual scheme that has been recently introduced by Jacinto and Scheimberg
(Optimization 57:795–805, 2008) for convex equilibrium problems. Through these schemes, as by products, we obtain new optimality
conditions for (GEP) and also, gap functions for (GEP), which cover the ones in Antangerel et al. (J Oper Res 24:353–371,
2007, Pac J Optim 2:667–678, 2006) for variational inequalities and standard convex equilibrium problems. These results, in
turn, when applied to DC and convex optimization problems with convex constraints (considered as special cases of (GEP)) lead
to Toland-Fenchel-Lagrange duality for DC problems in Dinh et al. (Optimization 1–20, 2008, J Convex Anal 15:235–262, 2008),
Fenchel-Lagrange and Lagrange dualities for convex problems as in Antangerel et al. (Pac J Optim 2:667–678, 2006), Bot and
Wanka (Nonlinear Anal to appear), Jeyakumar et al. (Applied Mathematics research report AMR04/8, 2004). Besides, as consequences
of the main results, we obtain some new optimality conditions for DC and convex problems. 相似文献
17.
Multicriteria games describe strategic interactions in which players, having more than one criterion to take into account,
don’t have an a-priori opinion on the relative importance of all these criteria. Roemer (Econ. Bull. 3:1–13, 2005) introduces an organizational interpretation of the concept of equilibrium: each player can be viewed as running a bargaining
game among criteria. In this paper, we analyze the bargaining problem within each player by considering the Kalai-Smorodinsky
bargaining solution (see Kalai and Smorodinsky in Econometrica 43:513–518, 1975). We provide existence results for the so called Kalai-Smorodinsky bargaining solution equilibria for a general class of disagreement points which properly includes the one considered by Roemer (Econ. Bull. 3:1–13, 2005). Moreover we look at the refinement power of this equilibrium concept and show that it is an effective selection device even when combined with classical refinement
concepts based on stability with respect to perturbations; in particular, we consider the extension to multicriteria games
of the Selten’s trembling hand perfect equilibrium concept (see Selten in Int. J. Game Theory 4:25–55, 1975) and prove that perfect Kalai-Smorodinsky bargaining solution equilibria exist and properly refine both the perfect equilibria
and the Kalai-Smorodinsky bargaining solution equilibria. 相似文献
18.
J. H. Wang 《Journal of Optimization Theory and Applications》2011,148(1):125-145
The present paper is concerned with the convergence problems of Newton’s method and the uniqueness problems of singular points
for sections on Riemannian manifolds. Suppose that the covariant derivative of the sections satisfies the generalized Lipschitz
condition. The convergence balls of Newton’s method and the uniqueness balls of singular points are estimated. Some applications
to special cases, which include the Kantorovich’s condition and the γ-condition, as well as the Smale’s γ-theory for sections on Riemannian manifolds, are given. In particular, the estimates here are completely independent of the
sectional curvature of the underlying Riemannian manifold and improve significantly the corresponding ones due to Dedieu,
Priouret and Malajovich (IMA J. Numer. Anal. 23:395–419, 2003), as well as the ones in Li and Wang (Sci. China Ser. A. 48(11):1465–1478, 2005). 相似文献
19.
S. E. Derkachov 《Journal of Mathematical Sciences》2008,151(2):2880-2893
The general rational solution of the Yang-Baxter equation with the symmetry algebra sℓ(2) can be represented as a product of simpler building blocks called -operators. -operators are constructed explicitly and have simple structure. Using -operators, we construct the two-parametric Baxter’s Q-operator for the generic inhomogeneous XXX-spin chain. In the case
of a homogeneous XXX-spin chain, it is possible to reduce the general Q-operator to a much simpler one-parametric Q-operator.
Bibliography: 22 titles.
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 347, 2007, pp. 144–166. 相似文献
20.
Laurent Lamy 《International Journal of Game Theory》2010,39(3):503-510
Day and Milgrom (Int J Game Theory 36:393–407, 2008) argue that package auctions that select the seller’s minimum revenue
in the Core are revenue-monotone. We show that no bidder-optimal Core-selecting auction can satisfy revenue-monotonicity for
general preferences when there are at least three goods for sale, while the property holds for any bidder-optimal Core-selecting
auction in environments with only two goods or if the characteristic function is submodular. 相似文献