Convergence analysis of a nonlinear Lagrangian algorithm for nonlinear programming with inequality constraints

2003 ◽  
Vol 13 (1-2) ◽  
pp. 1-10 ◽  
Author(s):  
Li-Wei Zhang ◽  
Yong-Jin Liu
Keyword(s):  
Nonlinear Programming ◽  
Convergence Analysis ◽  
Inequality Constraints ◽  
Nonlinear Lagrangian ◽  
Nonlinear Lagrangian Algorithm

scholarly journals Second-Order Multiplier Iteration Based on a Class of Nonlinear Lagrangians

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Yong-Hong Ren
Keyword(s):  
Nonlinear Programming ◽  
Optimization Problems ◽  
Inequality Constraints ◽  
Second Order ◽  
Constrained Optimization Problems ◽  
Lipschitz Continuous ◽  
First Order ◽  
Nonlinear Lagrangians ◽  
Nonlinear Lagrangian ◽  
Nonlinear Lagrangian Algorithm

Nonlinear Lagrangian algorithm plays an important role in solving constrained optimization problems. It is known that, under appropriate conditions, the sequence generated by the first-order multiplier iteration converges superlinearly. This paper aims at analyzing the second-order multiplier iteration based on a class of nonlinear Lagrangians for solving nonlinear programming problems with inequality constraints. It is suggested that the sequence generated by the second-order multiplier iteration converges superlinearly with order at least two if in addition the Hessians of functions involved in problem are Lipschitz continuous.

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.

scholarly journals A Fritz John type sufficient optimality theorem in complex space

1974 ◽  
Vol 11 (2) ◽  
pp. 219-224 ◽  
Author(s):  
T.R. Gulati
Keyword(s):  
Nonlinear Programming ◽  
Complex Space ◽  
Inequality Constraints ◽  
Polyhedral Cones ◽  
Finite Dimensional

A Fritz John type sufficient optimality theorem is proved for nonlinear programming problems in finite dimensional complex space over polyhedral cones, which may include equality as well as inequality constraints.

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