A new augmented Lagrangian function for inequality constraints in nonlinear programming problems

1982 ◽  
Vol 36 (4) ◽  
pp. 495-519 ◽  
Author(s):  
G. Di Pillo ◽  
L. Grippo
Keyword(s):  
Nonlinear Programming ◽  
Augmented Lagrangian ◽  
Inequality Constraints ◽  
Lagrangian Function ◽  
Augmented Lagrangian Function

Exact augmented lagrangian function for nonlinear programming problems with inequality constraints

2005 ◽  
Vol 26 (12) ◽  
pp. 1649-1656 ◽  
Author(s):  
Xue-wu Du ◽  
Lian-sheng Zhang ◽  
You-lin Shang ◽  
Ming-ming Li
Keyword(s):  
Nonlinear Programming ◽  
Augmented Lagrangian ◽  
Inequality Constraints ◽  
Lagrangian Function ◽  
Augmented Lagrangian Function

Local Saddle Points Theory of a New Augmented Lagrangians

2010 ◽  
Vol 121-122 ◽  
pp. 123-127
Author(s):  
Wen Ling Zhao ◽  
Jing Zhang ◽  
Jin Chuan Zhou
Keyword(s):  
Saddle Point ◽  
Augmented Lagrangian ◽  
Saddle Points ◽  
Optimal Solution ◽  
Inequality Constraints ◽  
Lagrangian Function ◽  
Augmented Lagrangians ◽  
Augmented Lagrangian Function ◽  
Primal Problem ◽  
Local Optimal Solution

In connection with Problem (P) with both the equality constraints and inequality constraints, we introduce a new augmented lagrangian function. We establish the existence of local saddle point under the weaker sufficient second order condition, discuss the relationships between local optimal solution of the primal problem and local saddle point of the augmented lagrangian function.

A Class of Augumented Lagrangian Function for Nonlinear Programming

2011 ◽  
Vol 271-273 ◽  
pp. 1955-1960
Author(s):  
Mei Xia Li
Keyword(s):  
Nonlinear Programming ◽  
Programming Problem ◽  
Inequality Constraints ◽  
Unconstrained Minimization ◽  
Lagrangian Function ◽  
Point Of View ◽  
Theoretical Point ◽  
Non Linear Programming ◽  
Global Minimizers ◽  
Equality And Inequality Constraints

In this paper, we discuss an exact augumented Lagrangian functions for the non- linear programming problem with both equality and inequality constraints, which is the gen- eration of the augmented Lagrangian function in corresponding reference only for inequality constraints nonlinear programming problem. Under suitable hypotheses, we give the relation- ship between the local and global unconstrained minimizers of the augumented Lagrangian function and the local and global minimizers of the original constrained problem. From the theoretical point of view, the optimality solution of the nonlinear programming with both equality and inequality constraints and the values of the corresponding Lagrangian multipli- ers can be found by the well known method of multipliers which resort to the unconstrained minimization of the augumented Lagrangian function presented in this paper.

A Kind of NLP Algorithm with NCP Function

2011 ◽  
Vol 467-469 ◽  
pp. 877-881
Author(s):  
Ai Ping Jiang ◽  
Feng Wen Huang
Keyword(s):  
Optimization Problem ◽  
Augmented Lagrangian ◽  
Merit Function ◽  
Lagrangian Function ◽  
Filter Method ◽  
Augmented Lagrangian Function ◽  
Penalty Term ◽  
Ncp Function ◽  
Modified Algorithm ◽  
Constrained Function

In this paper, two modifications are proposed for minimizing the nonlinear optimization problem (NLP) based on Fletcher and Leyffer’s filter method which is different from traditional merit function with penalty term. We firstly modify one component of filter pairs with NCP function instead of violation constrained function in order to avoid the difficulty of selecting penalty parameters. We also proved that the modified algorithm is globally and super linearly convergent under certain conditions. We secondly convert objective function to augmented Lagrangian function in case of incompatibility caused by sub-problems.

scholarly journals Existence of Local Saddle Points for a New Augmented Lagrangian Function

2010 ◽  
Vol 2010 ◽  
pp. 1-13 ◽  
Author(s):  
Wenling Zhao ◽  
Jing Zhang ◽  
Jinchuan Zhou
Keyword(s):  
Augmented Lagrangian ◽  
Saddle Points ◽  
Optimal Solution ◽  
Inequality Constraints ◽  
Augmented Lagrangian Function ◽  
Lagrangian Functions ◽  
New Class ◽  
Close Relationship ◽  
Equality And Inequality Constraints ◽  
Local Optimal Solution

We give a new class of augmented Lagrangian functions for nonlinear programming problem with both equality and inequality constraints. The close relationship between local saddle points of this new augmented Lagrangian and local optimal solutions is discussed. In particular, we show that a local saddle point is a local optimal solution and the converse is also true under rather mild conditions.

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