A Short Note on a Path-Following Interpretation of the Primal-Dual Algorithm

2022 ◽  
pp. 407-411
Author(s):  
Patrick Tobin ◽  
Santosh Kumar
Keyword(s):  
Short Note ◽  
Path Following ◽  
Dual Algorithm ◽  
Primal Dual

scholarly journals Convergence of a short-step primal-dual algorithm based on the Gauss-Newton direction

2003 ◽  
Vol 2003 (10) ◽  
pp. 517-534 ◽  
Author(s):  
Serge Kruk ◽  
Henry Wolkowicz
Keyword(s):  
Optimal Solution ◽  
Path Following ◽  
Singular Value ◽  
Dual Algorithm ◽  
Strict Complementarity ◽  
Semidefinite Programs ◽  
Primal Dual ◽  
Newton Direction ◽  
Proof Of Convergence ◽  
Smallest Singular Value

We prove the theoretical convergence of a short-step, approximate path-following, interior-point primal-dual algorithm for semidefinite programs based on the Gauss-Newton direction obtained from minimizing the norm of the perturbed optimality conditions. This is the first proof of convergence for the Gauss-Newton direction in this context. It assumes strict complementarity and uniqueness of the optimal solution as well as an estimate of the smallest singular value of the Jacobian.

Study of a primal-dual algorithm for equality constrained minimization

2014 ◽  
Vol 59 (3) ◽  
pp. 405-433 ◽  
Author(s):  
Paul Armand ◽  
Joël Benoist ◽  
Riadh Omheni ◽  
Vincent Pateloup
Keyword(s):  
Constrained Minimization ◽  
Dual Algorithm ◽  
Primal Dual

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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