General central path and the largest step general central path following algorithm for linear programming

2001 ◽  
Vol 17 (3) ◽  
pp. 296-303
Author(s):  
Ai Wenbao ◽  
Zhang Kecun
Keyword(s):  
Linear Programming ◽  
Path Following ◽  
Central Path ◽  
Path Following Algorithm

A corrector–predictor path-following algorithm for semidefinite optimization

2014 ◽  
Vol 07 (02) ◽  
pp. 1450028 ◽  
Author(s):  
Behrouz Kheirfam
Keyword(s):  
Line Search ◽  
Optimization Problems ◽  
Path Following ◽  
Central Path ◽  
Semidefinite Optimization ◽  
Iteration Complexity ◽  
Proximity Measure ◽  
Corrector Step ◽  
Predictor Step ◽  
Path Following Algorithm

A corrector–predictor algorithm is proposed for solving semidefinite optimization problems. In each two steps, the algorithm uses the Nesterov–Todd directions. The algorithm produces a sequence of iterates in a neighborhood of the central path based on a new proximity measure. The predictor step uses line search schemes requiring the reduction of the duality gap, while the corrector step is used to restore the iterates to the neighborhood of the central path. Finally, the algorithm has [Formula: see text] iteration complexity.

A relaxed primal-dual path-following algorithm for linear programming

1996 ◽  
Vol 62 (1) ◽  
pp. 173-196
Author(s):  
Tsung-Min Hwang ◽  
Chih-Hung Lin ◽  
Wen-Wei Lin ◽  
Shu-Cherng Fang
Keyword(s):  
Linear Programming ◽  
Path Following ◽  
Primal Dual ◽  
Path Following Algorithm

A New Infinity-Norm Path Following Algorithm for Linear Programming

1995 ◽  
Vol 5 (2) ◽  
pp. 236-246 ◽  
Author(s):  
Kurt M. Anstreicher ◽  
Robert A. Bosch
Keyword(s):  
Linear Programming ◽  
Path Following ◽  
Infinity Norm ◽  
Path Following Algorithm

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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