A finite method for globally minimizing a concave function over an unbounded polyhedral convex set and its applications

1988 ◽  
Vol 52 (1-2) ◽  
pp. 21-36 ◽  
Author(s):  
T. V. Thieu
Keyword(s):  
Convex Set ◽  
Concave Function ◽  
Polyhedral Convex ◽  
Finite Method ◽  
Polyhedral Convex Set

scholarly journals On two problems over polyhedral convex sets

2015 ◽  
Vol 1 (1) ◽  
pp. 9-15
Author(s):  
Tran Vu Thieu
Keyword(s):  
Convex Sets ◽  
Convex Set ◽  
Linear Constraints ◽  
Concave Programming ◽  
Linear Equality ◽  
Polyhedral Convex ◽  
Polyhedral Convex Sets ◽  
Polyhedral Convex Set

In this paper, we are concerned with the following two problems often encountered in concave programming: Given the  vertices and extreme detections of a polyhedral convex set Modefined by a system of linear constraints, determine the vertices and  extreme directions of the polyhedral convex set  obtained from M just by adding one new linear equality (or inequality) constraint.Among the constraints of a given polyhedral convex set, find those which are redundant, i.e. which can be removed without affecting the polyhedral convex set.

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