A generalized gradient projection method for optimization problems with equality and inequality constraints about arbitrary initial point

1996 ◽  
Vol 12 (1) ◽  
pp. 40-49 ◽  
Author(s):  
Ziyou Gao ◽  
Yanlian Lai ◽  
Zongying Hu
Keyword(s):  
Projection Method ◽  
Optimization Problems ◽  
Initial Point ◽  
Inequality Constraints ◽  
Gradient Projection ◽  
Gradient Projection Method ◽  
Generalized Gradient ◽  
Equality And Inequality Constraints ◽  
Arbitrary Initial Point ◽  
Generalized Gradient Projection Method

scholarly journals Extension of Modified Polak-Ribière-Polyak Conjugate Gradient Method to Linear Equality Constraints Minimization Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Zhifeng Dai
Keyword(s):  
Conjugate Gradient Method ◽  
Projection Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problems ◽  
Equality Constraints ◽  
Gradient Projection ◽  
Gradient Projection Method ◽  
Linear Equality Constraints ◽  
Linear Equality

Combining the Rosen gradient projection method with the two-term Polak-Ribière-Polyak (PRP) conjugate gradient method, we propose a two-term Polak-Ribière-Polyak (PRP) conjugate gradient projection method for solving linear equality constraints optimization problems. The proposed method possesses some attractive properties: (1) search direction generated by the proposed method is a feasible descent direction; consequently the generated iterates are feasible points; (2) the sequences of function are decreasing. Under some mild conditions, we show that it is globally convergent with Armijio-type line search. Preliminary numerical results show that the proposed method is promising.

The Gradient Projection Method under Mild Differentiability Conditions

1972 ◽  
Vol 10 (1) ◽  
pp. 93-98 ◽  
Author(s):  
G. P. McCormick ◽  
R. A. Tapia
Keyword(s):  
Projection Method ◽  
Gradient Projection ◽  
Gradient Projection Method
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