A SUFFICIENT MINIMALITY CONDITION FOR CONVEX COMPOSITE FUNCTIONS

2017 ◽  
Vol 97 (2-3) ◽  
pp. 75-83
Author(s):  
Stefan Hamann
2011 ◽  
Vol 19 (4-5) ◽  
pp. 401-404
Author(s):  
Dai Yao ◽  
Zhang Lei ◽  
Liu Jun-feng ◽  
Zhong Xiao

2021 ◽  
Vol 78 (1) ◽  
pp. 139-156
Author(s):  
Antonio Boccuto

Abstract We give some versions of Hahn-Banach, sandwich, duality, Moreau--Rockafellar-type theorems, optimality conditions and a formula for the subdifferential of composite functions for order continuous vector lattice-valued operators, invariant or equivariant with respect to a fixed group G of homomorphisms. As applications to optimization problems with both convex and linear constraints, we present some Farkas and Kuhn-Tucker-type results.


1994 ◽  
Vol 17 (5) ◽  
pp. 393-408
Author(s):  
Kim S. Larsen ◽  
Michael I. Schwartzbach
Keyword(s):  

2010 ◽  
Vol 18 (2) ◽  
pp. 129-141
Author(s):  
Bo Li ◽  
Na Ma ◽  
Xiquan Liang

Integrability Formulas. Part II In this article, we give several differentiation and integrability formulas of special and composite functions including trigonometric function, and polynomial function.


2001 ◽  
Vol 30 (1) ◽  
pp. 34-58
Author(s):  
Laura J. Downing

A body of work in Prosodic Morphology clearly establishes the importance of prosodic constituents like the foot as templates conditioning morpheme size. A striking finding of this research is that morphological footing is independent of metrical footing in many languages, as the footing required for particular morphological processes is often not identical to that required for phonological processes like stress assignment. However, recent OT research on Prosodic Morphology has made the opposite claim. Within this theory, the Generalized Template Hypothesis (GTH) proposes that no morpheme-particular templates defining minimal and maximal size are necessary. Instead, templates are always derivable from general principles of the grammar, like independently motivated metrical footing. This paper presents evidence from Ndebele showing that the GTH is too strong. In Ndebele, several different verb forms are subject to a minimality condition. In some cases, the minimality condition can be derived through independent metrical footing, as the GTH predicts. However, in several cases it cannot, showing that morpheme-particular size constraints are still a necessary part of the grammar.


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