scholarly journals The sharpening of some inequalities via abstract convexity

2009 ◽  
pp. 33-51 ◽  
Author(s):  
Gabil Adilov ◽  
Gültekin Tinaztepe
Keyword(s):  
Abstract Convexity

Zero duality gap conditions via abstract convexity∗

Optimization ◽  
2021 ◽  
pp. 1-37
Author(s):  
Hoa T. Bui ◽  
Regina S. Burachik ◽  
Alexander Y. Kruger ◽  
David T. Yost
Keyword(s):  
Duality Gap ◽  
Abstract Convexity ◽  
Zero Duality Gap

scholarly journals A further characteristic of abstract convexity structures on topological spaces

2007 ◽  
Vol 335 (1) ◽  
pp. 716-723 ◽  
Author(s):  
Shu-wen Xiang ◽  
Shunyou Xia
Keyword(s):  
Abstract Convexity ◽  
Topological Spaces

scholarly journals A sharpened version of Aczél inequality by abstract convexity

2021 ◽  
pp. 635-643
Author(s):  
Ramazan Tinaztepe ◽  
Gultekin Tinaztepe
Keyword(s):  
Abstract Convexity

Further investigation of abstract convexity with respect to the class of general min-type functions

Optimization ◽  
2007 ◽  
Vol 56 (1-2) ◽  
pp. 129-147 ◽  
Author(s):  
A. P. Shveidel
Keyword(s):  
Abstract Convexity

scholarly journals Abstract convexity and generalizations of Himmelberg type fixed-point theorems

2001 ◽  
Vol 41 (3-4) ◽  
pp. 497-504 ◽  
Author(s):  
Ping Ding Xie
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Abstract Convexity

scholarly journals On duality for nonconvex minimization problems within the framework of abstract convexity

Optimization ◽  
2021 ◽  
pp. 1-23
Author(s):  
Ewa M. Bednarczuk ◽  
Monika Syga
Keyword(s):  
Abstract Convexity ◽  
Nonconvex Minimization ◽  
Minimization Problems

scholarly journals Robust strong duality for nonconvex optimization problem under data uncertainty in constraint

2021 ◽  
Vol 6 (11) ◽  
pp. 12321-12338
Author(s):  
Yanfei Chai ◽  
Keyword(s):  
Nonconvex Optimization ◽  
Optimization Problem ◽  
Conjugate Function ◽  
Strong Duality ◽  
Data Uncertainty ◽  
Abstract Convexity ◽  
Conjugate Duality ◽  
Dual Problems ◽  
Uncertain Optimization ◽  
Robust Strong Duality

<abstract><p>This paper deals with the robust strong duality for nonconvex optimization problem with the data uncertainty in constraint. A new weak conjugate function which is abstract convex, is introduced and three kinds of robust dual problems are constructed to the primal optimization problem by employing this weak conjugate function: the robust augmented Lagrange dual, the robust weak Fenchel dual and the robust weak Fenchel-Lagrange dual problem. Characterizations of inequality (1.1) according to robust abstract perturbation weak conjugate duality are established by using the abstract convexity. The results are used to obtain robust strong duality between noncovex uncertain optimization problem and its robust dual problems mentioned above, the optimality conditions for this noncovex uncertain optimization problem are also investigated.</p></abstract>

Topical and sub-topical functions, downward sets and abstract convexity

Optimization ◽  
2001 ◽  
Vol 50 (5-6) ◽  
pp. 307-351 ◽  
Author(s):  
A. M. Rubinov ◽  
I. Singer
Keyword(s):  
Abstract Convexity
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