Path-Following Methods for Linear Programming

SIAM Review ◽  
1992 ◽  
Vol 34 (2) ◽  
pp. 167-224 ◽  
Author(s):  
Clovis C. Gonzaga
Keyword(s):  
Linear Programming ◽  
Path Following ◽  
Path Following Methods

On the generalized path-following methods for linear programming

Optimization ◽  
1994 ◽  
Vol 30 (3) ◽  
pp. 235-249 ◽  
Author(s):  
R. L. Sheu ◽  
S. C. Fang
Keyword(s):  
Linear Programming ◽  
Path Following ◽  
Path Following Methods

Fuzzy Heuristics for Sequential Linear Programming

1998 ◽  
Vol 120 (1) ◽  
pp. 17-23 ◽  
Author(s):  
E. L. Mulkay ◽  
S. S. Rao
Keyword(s):  
Fuzzy Logic ◽  
Linear Programming ◽  
Path Following ◽  
Human Observer ◽  
Sequential Linear Programming ◽  
Algorithm Performance ◽  
Primal Dual ◽  
Improve Algorithm ◽  
Range Of Values ◽  
Better Than

Numerical implementations of optimization algorithms often use parameters whose values are not strictly determined by the derivation of the algorithm, but must fall in some appropriate range of values. This work describes how fuzzy logic can be used to “control” such parameters to improve algorithm performance. This concept is shown with the use of sequential linear programming (SLP) due to its simplicity in implementation. The algorithm presented in this paper implements heuristics to improve the behavior of SLP based on current iterate values of design constraints and changes in search direction. Fuzzy logic is used to implement the heuristics in a form similar to what a human observer would do. An efficient algorithm, known as the infeasible primal-dual path-following interior-point method, is used for solving the sequence of LP problems. Four numerical examples are presented to show that the proposed SLP algorithm consistently performs better than the standard SLP algorithm.

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