scholarly journals Strong Duality Property for Matroids with Coefficients

1994 ◽  
Vol 15 (3) ◽  
pp. 293-302 ◽  
Author(s):  
Marc Wagowski
Author(s):  
Olga I. Kostyukova ◽  
Tatiana V. Tchemisova

Regularisation consists in reducing a given optimisation problem to an equivalent form where certain regularity conditions, which guarantee the strong duality, are fulfilled. In this paper, for linear problems of semidefinite programming (SDP), we propose a regularisation procedure which is based on the concept of an immobile index set and its properties. This procedure is described in the form of a finite algorithm which converts any linear semidefinite problem to a form that satisfies the Slater condition. Using the properties of the immobile indices and the described regularization procedure, we obtained new dual SDP problems in implicit and explicit forms. It is proven that for the constructed dual problems and the original problem the strong duality property holds true.


Literator ◽  
1992 ◽  
Vol 13 (1) ◽  
pp. 15-28 ◽  
Author(s):  
H. Viljoen

This article is an attempt to outline the difference between Breytenbach's poetic method and that of the Symbolists. Although it touches on aspects of the symbolist poetic method like the rich suggestiveness, the creation o f a meaningful alternative world (and the effort of doing this), it focuses mainly on Breytenbach’s use of metaphor to create an impossible alternative world in a poem, only to relativize and destroy it again in the end. This process is illustrated in an analysis of poem 8.1 from Lotus. This analysis also shows up five well-known cardinal traits of Breytenbach’s poetry, viz. its carnality, the universal analogy between body, cosmos and poetry and the great emphasis on journeys, discoveries and transformations by means of language. It is also claimed that the Zen-Buddhisi Void plays an analogous role in Breytenbach's poetry to the theory of correspondances in the Symbolists: it is a rich source of metaphor. Breytenbach's poetry shows a strong duality between the present world and a meaningful alternative sphere. Being in and of this alternative sphere only aggravates the poet’s isolation (a typically symbolist trait), making him literally and figuratively an exile, as exile poems like "tot siens, kaapstad" (see you again, cape town) and "Walvis in die berg" (Whale on the mountain) and, of course, his prison poetry, clearly show.


Author(s):  
XIANG LI ◽  
BAODING LIU

Possibility measures and credibility measures are widely used in fuzzy set theory. Compared with possibility measures, the advantage of credibility measures is the self-duality property. This paper gives a relation between possibility measures and credibility measures, and proves a sufficient and necessary condition for credibility measures. Finally, the credibility extension theorem is shown.


2002 ◽  
Vol 73 (3) ◽  
pp. 377-392 ◽  
Author(s):  
R. Quackenbush ◽  
C. S. Szabó

AbstractDavey and Quackenbush proved a strong duality for each dihedral group Dm with m odd. In this paper we extend this to a strong duality for each finite group with cyclic Sylow subgroups (such groups are known to be metacyclic).


2011 ◽  
Vol 77 (3-4) ◽  
pp. 513-524
Author(s):  
Belmesnaoui Aqzzouz ◽  
Aziz Elbour

1979 ◽  
Vol 20 (2) ◽  
pp. 301-312
Author(s):  
T.R. Jefferson ◽  
C.H. Scott

For convex optimal control problems without explicit pure state constraints, the structure of dual problems is now well known. However, when these constraints are present and active, the theory of duality is not highly developed. The major difficulty is that the dual variables are not absolutely continuous functions as a result of singularities when the state trajectory hits a state constraint. In this paper we recognize this difficulty by formulating the dual probram in the space of measurable functions. A strong duality theorem is derived. This pairs a primal, state constrained convex optimal control problem with a dual convex control problem that is unconstrained with respect to state constraints. In this sense, the dual problem is computationally more attractive than the primal.


2010 ◽  
Vol 5 (4) ◽  
pp. 665-682 ◽  
Author(s):  
Yingnan Wang ◽  
Naihua Xiu ◽  
Ziyan Luo

2008 ◽  
Vol 80 (1) ◽  
pp. 3-19
Author(s):  
Shuguo Shi

In this paper, we introduce the fourth fundamental forms for hypersurfaces in Hn+1 and space-like hypersurfaces in S1n+1, and discuss the conformality of the normal Gauss map of the hypersurfaces in Hn+1 and S1n+1. Particularly, we discuss the surfaces with conformal normal Gauss map in H³ and S³1, and prove a duality property. We give a Weierstrass representation formula for space-like surfaces in S³1 with conformal normal Gauss map. We also state the similar results for time-like surfaces in S³1. Some examples of surfaces in S³1 with conformal normal Gauss map are given and a fully nonlinear equation of Monge-Ampère type for the graphs in S³1 with conformal normal Gauss map is derived.


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