Minimization of extended quadratic functions with inexact line searches

1994 ◽  
Vol 82 (1) ◽  
pp. 139-147 ◽  
Author(s):  
N. H. Al-Assady ◽  
A. Y. Al-Bayati
Keyword(s):  
Quadratic Functions ◽  
Line Searches ◽  
Inexact Line Searches

A Hybrid Variable Metric Update for the Recursive Quadratic Programming Method

1991 ◽  
Vol 113 (3) ◽  
pp. 280-285 ◽  
Author(s):  
T. J. Beltracchi ◽  
G. A. Gabriele
Keyword(s):  
Quadratic Programming ◽  
Optimization Problems ◽  
Variable Metric ◽  
Hybrid Variable ◽  
Recursive Quadratic Programming ◽  
Line Searches ◽  
Inexact Line Searches ◽  
Rank One ◽  
Symmetric Rank One ◽  
Quadratic Programming Method

The Recursive Quadratic Programming (RQP) method has become known as one of the most effective and efficient algorithms for solving engineering optimization problems. The RQP method uses variable metric updates to build approximations of the Hessian of the Lagrangian. If the approximation of the Hessian of the Lagrangian converges to the true Hessian of the Lagrangian, then the RQP method converges quadratically. The choice of a variable metric update has a direct effect on the convergence of the Hessian approximation. Most of the research performed with the RQP method uses some modification of the Broyden-Fletcher-Shanno (BFS) variable metric update. This paper describes a hybrid variable metric update that yields good approximations to the Hessian of the Lagrangian. The hybrid update combines the best features of the Symmetric Rank One and BFS updates, but is less sensitive to inexact line searches than the BFS update, and is more stable than the SR1 update. Testing of the method shows that the efficiency of the RQP method is unaffected by the new update but more accurate Hessian approximations are produced. This should increase the accuracy of the solutions obtained with the RQP method, and more importantly, provide more reliable information for post optimality analyses, such as parameter sensitivity studies.

scholarly journals A gradient-related algorithm with inexact line searches

2004 ◽  
Vol 170 (2) ◽  
pp. 349-370 ◽  
Author(s):  
Zhen-Jun Shi ◽  
Jie Shen
Keyword(s):  
Line Searches ◽  
Inexact Line Searches

Full convergence of the steepest descent method with inexact line searches

Optimization ◽  
1995 ◽  
Vol 32 (2) ◽  
pp. 137-146 ◽  
Author(s):  
R. Burachik ◽  
L. M. Graña Drummond ◽  
A.N. Iusem ◽  
B. F. Svaiter
Keyword(s):  
Descent Method ◽  
Steepest Descent ◽  
Steepest Descent Method ◽  
Line Searches ◽  
Inexact Line Searches

scholarly journals New multi-step three-term conjugate gradient algorithms with inexact line searches

2020 ◽  
Vol 19 (3) ◽  
pp. 1564
Author(s):  
Abbas Younis Al-Bayati ◽  
Muna M. M. Ali
Keyword(s):  
Conjugate Gradient ◽  
Line Search ◽  
Conjugate Gradient Algorithms ◽  
Line Searches ◽  
Gradient Algorithms ◽  
Inexact Line Searches ◽  
Sufficient Descent ◽  
Strong Wolfe Line Search ◽  
Wolfe Line Search ◽  
Memoryless Bfgs Update

<p>This work suggests several multi-step three-term Conjugate Gradient (CG)-algorithms that satisfies their sufficient descent property and conjugacy conditions. First, we have  considered a number of well-known three-term CG-method, and we have, therefore, suggested two new classes of this type of algorithms which was based on Hestenes and Stiefel (HS) and Polak-Ribière (PR) formulas with four different versions. Both descent and conjugacy conditions for all the proposed algorithms are satisfied, at each iteration by using the strong Wolfe line search condition and it's accelerated version. These new suggested algorithms are some sort of modifications to the original  HS and PR  methods. These CG-algorithms are considered as a sort of the  memoryless BFGS update.  All of our new suggested methods are proved to be a  global convergent and numerically, more efficient than the similar methods in same area based on our selected set of used numerical problems.</p>

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