Rotation Averaging with the Chordal Distance: Global Minimizers and Strong Duality

Author(s):  
Anders Eriksson ◽  
Carl Olsson ◽  
Fredrik Kahl ◽  
Tat-Jun Chin
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.


2015 ◽  
Vol 07 (02) ◽  
pp. 261-291 ◽  
Author(s):  
Jan Philipp Schröder

We study action-minimizing orbits in Tonelli Lagrangian systems on the 2-torus on fixed energy levels above Mañé's strict critical value. Our work generalizes the results of Morse, Hedlund and Bangert on minimal geodesics in Riemannian 2-tori. The techniques in the proofs involve classical variational ones, as well as the theories of Mather, Mañé and Fathi, which allow the step from reversible to non-reversible dynamics.


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).


Author(s):  
Alexander Murray ◽  
Timm Faulwasser ◽  
Veit Hagenmeyer ◽  
Mario E. Villanueva ◽  
Boris Houska

AbstractThis paper presents a novel partially distributed outer approximation algorithm, named PaDOA, for solving a class of structured mixed integer convex programming problems to global optimality. The proposed scheme uses an iterative outer approximation method for coupled mixed integer optimization problems with separable convex objective functions, affine coupling constraints, and compact domain. PaDOA proceeds by alternating between solving large-scale structured mixed-integer linear programming problems and partially decoupled mixed-integer nonlinear programming subproblems that comprise much fewer integer variables. We establish conditions under which PaDOA converges to global minimizers after a finite number of iterations and verify these properties with an application to thermostatically controlled loads and to mixed-integer regression.


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

Author(s):  
E. Parsopoulos Konstantinos ◽  
N. Vrahatis Michael

In the previous chapters, we presented the fundamental concepts and variants of PSO, as along with a multitude of recent research results. The reported results suggest that PSO can be a very useful tool for solving optimization problems from different scientific and technological fields, especially in cases where classical optimization methods perform poorly or their application involves formidable technical difficulties due to the problem’s special structure or nature. PSO was capable of addressing continuous and integer optimization problems, handling noisy and multiobjective cases, and producing efficient hybrid schemes in combination with specialized techniques or other algorithms in order to detect multiple (local or global) minimizers or control its own parameters.


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