Sequential convexification in reverse convex and disjunctive programming

1989 ◽  
Vol 44 (1-3) ◽  
pp. 337-350 ◽  
Author(s):  
Egon Balas ◽  
Joseph M. Tama ◽  
Jørgen Tind
Keyword(s):  
Disjunctive Programming ◽  
Reverse Convex

scholarly journals Asymptotic Farkas lemmas for convex systems

2016 ◽  
Vol 19 (4) ◽  
pp. 160-168
Author(s):  
Dinh Nguyen ◽  
Mo Hong Tran
Keyword(s):  
Vector Space ◽  
Topological Vector Space ◽  
Constraint Qualification ◽  
Convex Set ◽  
Lower Semicontinuous ◽  
Closed Convex Cone ◽  
Convex Mapping ◽  
Hausdorff Topological Vector Space ◽  
Reverse Convex ◽  
Locally Convex

In this paper we establish characterizations of the containment of the set {xX: xC,g(x)K}{xX: f (x)0}, where C is a closed convex subset of a locally convex Hausdorff topological vector space, X, K is a closed convex cone in another locally convex Hausdorff topological vector space and g:X Y is a K- convex mapping, in a reverse convex set, define by the proper, lower semicontinuous, convex function. Here, no constraint qualification condition or qualification condition are assumed. The characterizations are often called asymptotic Farkas-type results. The second part of the paper was devoted to variant Asymptotic Farkas-type results where the mapping is a convex mapping with respect to an extended sublinear function. It is also shown that under some closedness conditions, these asymptotic Farkas lemmas go back to non-asymptotic Farkas lemmas or stable Farkas lemmas established recently in the literature. The results can be used to study the optimization

scholarly journals Optimization of Discrete-Continuous Dynamic Systems Based on Disjunctive Programming

PAMM ◽  
2005 ◽  
Vol 5 (1) ◽  
pp. 51-54 ◽  
Author(s):  
Jan Oldenburg ◽  
Wolfgang Marquardt
Keyword(s):  
Dynamic Systems ◽  
Disjunctive Programming ◽  
Continuous Dynamic
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