Sufficient condition of basis stability of an interval linear programming problem

2001 ◽  
Vol 81 (S3) ◽  
pp. 677-678 ◽  
Author(s):  
Jana Koníckocá
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Sufficient Condition ◽  
Interval Linear Programming ◽  
Interval Linear

Construction Method of Constraint Matrices Corresponded by an Optimal Solution

2014 ◽  
Vol 513-517 ◽  
pp. 1617-1620
Author(s):  
Xiao Liu ◽  
Wei Li ◽  
Peng Zhen Liu
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Linear Equations ◽  
Optimal Solution ◽  
Construction Method ◽  
Interval Linear Programming ◽  
Interval Linear

Through deep analysis of the solvability, which is based on interval linear equations and inequalities systems, for a given optimal solution to interval linear programming problem, we propose the construction method of constraint matrices corresponded by the optimal solution in this paper.

scholarly journals Linear programming with positive semi-definite matrices

1996 ◽  
Vol 2 (6) ◽  
pp. 499-522 ◽  
Author(s):  
J. B. Lasserre
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Feasible Solution ◽  
Extreme Points ◽  
Duality Gap ◽  
Sufficient Condition ◽  
Optimal Solutions ◽  
Existence Of Optimal Solutions ◽  
Simple Sufficient Condition

We consider the general linear programming problem over the cone of positive semi-definite matrices. We first provide a simple sufficient condition for existence of optimal solutions and absence of a duality gap without requiring existence of a strictly feasible solution. We then simply characterize the analogues of the standard concepts of linear programming, i.e., extreme points, basis, reduced cost, degeneracy, pivoting step as well as a Simplex-like algorithm.

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