scholarly journals $$\rho$$-regularization subproblems: strong duality and an eigensolver-based algorithm

Author(s):  
Liaoyuan Zeng ◽  
Ting Kei Pong
Keyword(s):  
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.


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).


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

2017 ◽  
Vol 69 (4) ◽  
pp. 823-845 ◽  
Author(s):  
Fabián Flores-Bazán ◽  
William Echegaray ◽  
Fernando Flores-Bazán ◽  
Eladio Ocaña

Author(s):  
Kenneth O. Kortanek ◽  
Guolin Yu ◽  
Qinghong Zhang

2020 ◽  
Vol 14 (8) ◽  
pp. 1989-2006
Author(s):  
Ron Estrin ◽  
Michael P. Friedlander

Abstract Level-set methods for convex optimization are predicated on the idea that certain problems can be parameterized so that their solutions can be recovered as the limiting process of a root-finding procedure. This idea emerges time and again across a range of algorithms for convex problems. Here we demonstrate that strong duality is a necessary condition for the level-set approach to succeed. In the absence of strong duality, the level-set method identifies $$\epsilon $$ ϵ -infeasible points that do not converge to a feasible point as $$\epsilon $$ ϵ tends to zero. The level-set approach is also used as a proof technique for establishing sufficient conditions for strong duality that are different from Slater’s constraint qualification.


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