scholarly journals Technical Note—Comments on the “Classical” Derivation by Taha and Curry of Optimality Conditions in Linear Programming

1973 ◽  
Vol 21 (1) ◽  
pp. 371-372
Author(s):  
William M. Raike ◽  
James G. Taylor
Keyword(s):  
Linear Programming ◽  
Optimality Conditions ◽  
Technical Note ◽  
Classical Derivation

scholarly journals An improved three-step method for solving the interval linear programming problems

2018 ◽  
Vol 28 (4) ◽  
pp. 435-451 ◽  
Author(s):  
Mehdi Allahdadi ◽  
Chongyang Deng
Keyword(s):  
Linear Programming ◽  
Optimality Conditions ◽  
Optimality Condition ◽  
Solution Space ◽  
Interval Linear Programming ◽  
Step Method ◽  
Feasibility Condition ◽  
Extra Step ◽  
Interval Linear ◽  
Linear Programming Problems

Feasibility condition, which ensures that the solution space does not violate any constraints, and optimality condition, which guarantees that all points of the solution space are optimal, are very significant conditions for the solution space of interval linear programming (ILP) problems. Among the existing methods for ILP problems, the best-worst cases (BWC) method and two-step method (TSM) do not ensure feasibility condition, while the modified ILP (MILP), robust TSM (RTSM), improved TSM (ITSM), and three-step method (ThSM) guarantee feasibility condition, whose solution spaces may not be completely optimal. We propose an improved ThSM (IThSM) for ILP problems, which ensures both feasibility and optimality conditions, i.e., we introduce an extra step to optimality.

scholarly journals Technical Note—“Linear” Programming with Absolute-Value Functionals

1971 ◽  
Vol 19 (1) ◽  
pp. 120-124 ◽  
Author(s):  
David F. Shanno ◽  
Roman L. Weil
Keyword(s):  
Linear Programming ◽  
Technical Note ◽  
Absolute Value
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