Recursive quadratic programming algorithm that uses an exact augmented Lagrangian function

1990 ◽  
Vol 67 (2) ◽  
pp. 227-245 ◽  
Author(s):  
S. Lucidi
Keyword(s):  
Quadratic Programming ◽  
Augmented Lagrangian ◽  
Lagrangian Function ◽  
Programming Algorithm ◽  
Augmented Lagrangian Function ◽  
Recursive Quadratic Programming

Optimization With Discrete Variables Via Recursive Quadratic Programming: Part 2—Algorithm and Results

1989 ◽  
Vol 111 (1) ◽  
pp. 130-136 ◽  
Author(s):  
J. Z. Cha ◽  
R. W. Mayne
Keyword(s):  
Quadratic Programming ◽  
Performance Comparison ◽  
Programming Algorithm ◽  
Discrete Variables ◽  
Contour Analysis ◽  
Recursive Quadratic Programming ◽  
Analysis Technique ◽  
Rank One ◽  
Symmetric Rank One ◽  
Monotonicity Analysis

A discrete recursive quadratic programming algorithm is developed for a class of mixed discrete constrained nonlinear programming (MDCNP) problems. The symmetric rank one (SR1) Hessian update formula is used to generate second order information. Also, strategies, such as the watchdog technique (WT), the monotonicity analysis technique (MA), the contour analysis technique (CA), and the restoration of feasibility have been considered. Heuristic aspects of handling discrete variables are treated via the concepts and convergence discussions of Part I. This paper summarizes the details of the algorithm and its implementation. Test results for 25 different problems are presented to allow evaluation of the approach and provide a basis for performance comparison. The results show that the suggested method is a promising one, efficient and robust for the MDCNP problem.

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.

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

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.

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