Interior-Point Methodology for Linear Programming: Duality, Sensitivity Analysis and Computational Aspects

1993 ◽  
pp. 57-123 ◽  
Author(s):  
B. Jansen ◽  
C. Roos ◽  
T. Terlaky ◽  
J.-Ph. Vial
Keyword(s):  
Sensitivity Analysis ◽  
Linear Programming ◽  
Interior Point ◽  
Linear Programming Duality ◽  
Computational Aspects

ON THE PROPERTIES OF ∊-SENSITIVITY ANALYSIS FOR LINEAR PROGRAMMING

2005 ◽  
Vol 22 (02) ◽  
pp. 135-151 ◽  
Author(s):  
CHAN-KYOO PARK ◽  
WOO-JE KIM ◽  
SOONDAL PARK
Keyword(s):  
Sensitivity Analysis ◽  
Linear Programming ◽  
Interior Point ◽  
Interior Point Methods ◽  
Heuristic Method ◽  
Optimal Partition ◽  
Characteristic Region ◽  
Analysis Methods ◽  
Perform Sensitivity Analysis ◽  
Simplified Formula

∊-Sensitivity analysis (∊-SA) is a kind of method to perform sensitivity analysis for linear programming. Its main advantage is that it can be directly applied for interior-point methods with a little computation. In this paper, we discuss the property of ∊-SA analysis and its relationship with other sensitivity analysis methods. First, we present a new property of ∊-SA, from which we derive a simplified formula for finding the characteristic region of ∊-SA. Next, based on the simplified formula, we show that the characteristic region of ∊-SA includes the characteristic region of Yildirim and Todd's method. Finally, we show that the characteristic region of ∊-SA asymptotically becomes a subset of the characteristic region of sensitivity analysis using optimal partition. Our results imply that ∊-SA can be used as a practical heuristic method for approximating the characteristic region of sensitivity analysis using optimal partition.

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