A Global Convergence Theorem for Descent Algorithms

1995 ◽  
pp. 305-305
Author(s):  
Gerhard Winkler
Keyword(s):  
Global Convergence ◽  
Convergence Theorem ◽  
Descent Algorithms

scholarly journals The Global Convergence of the Nonlinear Power Method for Mixed-Subordinate Matrix Norms

2021 ◽  
Vol 88 (1) ◽  
Author(s):  
Antoine Gautier ◽  
Matthias Hein ◽  
Francesco Tudisco
Keyword(s):  
Global Convergence ◽  
Convergence Theorem ◽  
Matrix Norm ◽  
Nonnegative Matrices ◽  
Np Hard ◽  
Power Method ◽  
Contraction Ratio ◽  
Matrix Norms ◽  
Vector Norms

AbstractWe analyze the global convergence of the power iterates for the computation of a general mixed-subordinate matrix norm. We prove a new global convergence theorem for a class of entrywise nonnegative matrices that generalizes and improves a well-known results for mixed-subordinate $$\ell ^p$$ ℓ p matrix norms. In particular, exploiting the Birkoff–Hopf contraction ratio of nonnegative matrices, we obtain novel and explicit global convergence guarantees for a range of matrix norms whose computation has been recently proven to be NP-hard in the general case, including the case of mixed-subordinate norms induced by the vector norms made by the sum of different $$\ell ^p$$ ℓ p -norms of subsets of entries.

A global convergence theorem for aggregation algorithms

Optimization ◽  
1988 ◽  
Vol 19 (6) ◽  
pp. 819-828 ◽  
Author(s):  
L. García
Keyword(s):  
Global Convergence ◽  
Convergence Theorem

scholarly journals A GLOBAL CONVERGENCE THEOREM IN BOOLEAN ALGEBRA

2010 ◽  
Vol 14 (3B) ◽  
pp. 1135-1144 ◽  
Author(s):  
Juei-Ling Ho
Keyword(s):  
Global Convergence ◽  
Boolean Algebra ◽  
Convergence Theorem
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