A strong bound on the integral of the central path curvature and its relationship with the iteration-complexity of primal-dual path-following LP algorithms

2007 ◽  
Vol 115 (1) ◽  
pp. 105-149 ◽  
Author(s):  
Renato D. C. Monteiro ◽  
Takashi Tsuchiya
Keyword(s):  
Path Following ◽  
Central Path ◽  
Iteration Complexity ◽  
Strong Bound ◽  
Primal Dual ◽  
Path Curvature

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.

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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