Generalized memory gradient projection method for non-linear programming with non-linear equality and in-equality constraints

2010 ◽  
Vol 36 (1-2) ◽  
pp. 347-366
Author(s):  
Qingying Sun ◽  
Zhaoyang Sang
Keyword(s):  
Linear Programming ◽  
Projection Method ◽  
Equality Constraints ◽  
Gradient Projection ◽  
Gradient Projection Method ◽  
Non Linear Programming ◽  
Linear Equality ◽  
Non Linear

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.

A New Conjugate Gradient Projection Method and its Application

2013 ◽  
Vol 756-759 ◽  
pp. 3537-3541
Author(s):  
Hong Fang Cui ◽  
Ting Zhou
Keyword(s):  
Linear Model ◽  
Projection Method ◽  
Conjugate Gradient ◽  
Estimation Algorithm ◽  
Equality Constraints ◽  
Gradient Projection ◽  
Gradient Projection Method

This paper constructs a new P-DY conjugate gradient projection method, the parameter contains parameters, it can be good to adjust the parameters of, this method makes the problem much faster, and more accurate results can be obtained iteratively. The decline of this algorithm and search convergence principle under the condition of Wolfe line, and will test new estimation algorithm, it is applied to the linear model with equality constraints and the results show that the effect is very good.

scholarly journals Optimal allocation of stratified sampling design using Gradient Projection method

2017 ◽  
Vol 10 (1) ◽  
pp. 11-17
Author(s):  
M. A Lone ◽  
S. A Mir ◽  
Imran Khan ◽  
M. S Wani
Keyword(s):  
Projection Method ◽  
Iterative Procedure ◽  
Sampling Design ◽  
Optimal Allocation ◽  
Stratified Sampling ◽  
Gradient Projection ◽  
Integer Solution ◽  
Gradient Projection Method ◽  
Non Linear Programming ◽  
The Cost

This article deals with the problem of finding an optimal allocation of sample sizes in stratified sampling design to minimize the cost function. In this paper the iterative procedure of Rosen’s Gradient projection method is used to solve the Non linear programming problem (NLPP), when a non integer solution is obtained after solving the NLPP then Branch and Bound method provides an integer solution.

ON NON-QUADRATIC PENALTY FUNCTION FOR NON-LINEAR PROGRAMMING PROBLEM WITH EQUALITY CONSTRAINTS

2019 ◽  
Vol 7 (1) ◽  
pp. 23-28
Author(s):  
Raju Prajapati ◽  
Om Prakash Dubey ◽  
Ranjit Pradhan
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Penalty Method ◽  
Equality Constraints ◽  
Test Problems ◽  
Barrier Methods ◽  
Non Linear Programming ◽  
Non Linear ◽  
Quadratic Penalty Method

Purpose: The present paper focuses on the Non-Linear Programming Problem (NLPP) with equality constraints. NLPP with constraints could be solved by penalty or barrier methods. Methodology: We apply the penalty method to the NLPP with equality constraints only. The non-quadratic penalty method is considered for this purpose. We considered a transcendental i.e. exponential function for imposing the penalty due to the constraint violation. The unconstrained NLPP obtained in this way is then processed for further solution. An improved version of evolutionary and famous meta-heuristic Particle Swarm Optimization (PSO) is used for the same. The method is tested with the help of some test problems and mathematical software SCILAB. The solution is compared with the solution of the quadratic penalty method. Results: The results are also compared with some existing results in the literature.

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