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961.
Levent Tunçel 《Foundations of Computational Mathematics》2001,1(3):229-254
We generalize primal—dual interior-point methods for linear programming (LP) problems to the convex optimization problems
in conic form. Previously, the most comprehensive theory of symmetric primal—dual interior-point algorithms was given by Nesterov
and Todd for feasible regions expressed as the intersection of a symmetric cone with an affine subspace. In our setting, we
allow an arbitrary convex cone in place of the symmetric cone. Even though some of the impressive properties attained by Nesterov—Todd
algorithms are impossible in this general setting of convex optimization problems, we show that essentially all primal—dual
interior-point algorithms for LP can be extended easily to the general setting. We provide three frameworks for primal—dual
algorithms, each framework corresponding to a different level of sophistication in the algorithms. As the level of sophistication
increases, we demand better formulations of the feasible solution sets. Our algorithms, in return, attain provably better
theoretical properties. We also make a very strong connection to quasi-Newton methods by expressing the square of the symmetric
primal—dual linear transformation (the so-called scaling) as a quasi-Newton update in the case of the least sophisticated
framework.
August 25, 1999. Final version received: March 7, 2001. 相似文献
962.
关于某类Reinhardt域的Bergman核函数与解析自同构最大群 总被引:1,自引:0,他引:1
本文给出了Reinhardt域D={z=(z1,z2,z3)∈:|z1|2k+|z2|+|z3|2<1,k>0}的Bergman核函数,Bergman度量方阵及其解析自同构最大群。 相似文献
963.
In this paper, the famous Banach contraction principle and Caristi's fixed point theorem are generalized to the case of multi-valued mappings. Our results are extensions of the well-known Nadler's fixed point theorem [S.B. Nadler Jr., Multi-valued contraction mappings, Pacific J. Math. 30 (1969) 475-487], as well as of some Caristi type theorems for multi-valued operators, see [N. Mizoguchi, W. Takahashi, Fixed point theorems for multivalued mappings on complete metric spaces, J. Math. Anal. Appl. 141 (1989) 177-188; J.P. Aubin, Optima and Equilibria. An Introduction to Nonlinear Analysis, Grad. Texts in Math., Springer-Verlag, Berlin, 1998, p. 17; S.S. Zhang, Q. Luo, Set-valued Caristi fixed point theorem and Ekeland's variational principle, Appl. Math. Mech. 10 (2) (1989) 111-113 (in Chinese), English translation: Appl. Math. Mech. (English Ed.) 10 (2) (1989) 119-121], etc. 相似文献
964.
In this paper we examine the properties of EC-plastic metric spaces, spaces which have the property that any noncontractive bijection from the space onto itself must be an isometry. 相似文献
965.
In this paper, we study a class of vector minimization problems on a complete metric space X which is identified with the corresponding complete metric space of objective functions
. We do not impose any compactness assumption on X. We show that, for most (in the sense of Baire category) functions
, the corresponding vector optimization problem has a solution. 相似文献
966.
The study of extremal properties of the spectrum often involves restricting the metrics under consideration. Motivated by
the work of Abreu and Freitas in the case of the sphere S
2 endowed with S
1-invariant metrics, we consider the subsequence of the spectrum of a Riemannian manifold M which corresponds to metrics and functions invariant under the action of a compact Lie group G. If G has dimension at least 1, we show that the functional λ
k
G
admits no extremal metric under volume-preserving G-invariant deformations. If, moreover, M has dimension at least three, then the functional is unbounded when restricted to any conformal class of G-invariant metrics of fixed volume. As a special case of this, we can consider the standard O(n)-action on S
n
; however, if we also require the metric to be induced by an embedding of S
n
in , we get an optimal upper bound on .
相似文献
967.
Eduardo Chiumiento 《Integral Equations and Operator Theory》2008,62(3):365-382
We study the metric geometry of homogeneous reductive spaces of the unitary group of a finite von Neumann algebra with a non
complete Riemannian metric. The main result gives an abstract sufficient condition in order that the geodesics of the Levi-Civita
connection are locally minimal. Then, we show how this result applies to several examples.
To my family 相似文献
968.
本文在黎曼流形$(M,g)$的切丛$TM$ 上研究与参考文献[10]中平行的一类度量$G$以及相容的近复结构$J$.证明了切丛$TM$关于这些度量和相应的近复结构是局部共形近K\"{a}hler流形,并且把这些结构限制在单位切球丛上得到了切触度量结构的新例子. 相似文献
969.
§1. IntroductionTheheatkernelofamaniforldcontainsrichimformationofgeometryandanalysisofthemanifold.Recenty,manymathematiciansandphysistsareinterestedinthisfieldandalotofimportantresultsareobtained.LetPn(C)denotethesetofalln×ncomplexHermitepositivedef… 相似文献
970.
In this paper, we study the (α,β)-metrics of scalar flag curvature in the form of F = α + εβ + κβ^2/α (ε and k ≠ 0 are constants) and F = α^2/α-β. We prove that these two kinds of metrics are weak Berwaldian if and only if they are Berwaldian and their flag curvatures vanish. In this case, the metrics are locally Minkowskian. 相似文献