A class of trust region methods for linear inequality constrained optimization and its theory analysis: I. Algorithm and global convergence

1995 ◽  
Vol 10 (3) ◽  
pp. 287-296 ◽  
Author(s):  
Xiu Naihua
Keyword(s):  
Global Convergence ◽  
Constrained Optimization ◽  
Linear Inequality ◽  
Trust Region ◽  
Trust Region Methods ◽  
Theory Analysis ◽  
Inequality Constrained Optimization ◽  
Linear Inequality Constrained Optimization

scholarly journals A Nonmonotone Trust Region Algorithm Based on the Average of the Successive Penalty Function Values for Nonlinear Optimization

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Zhensheng Yu ◽  
Jinhong Yu
Keyword(s):  
Global Convergence ◽  
Penalty Function ◽  
Optimization Problems ◽  
Trust Region ◽  
Trust Region Methods ◽  
Constrained Optimization Problems ◽  
Trust Region Algorithm ◽  
Numerical Tests ◽  
Equality Constrained Optimization ◽  
Nonlinear Equality

We present a nonmonotone trust region algorithm for nonlinear equality constrained optimization problems. In our algorithm, we use the average of the successive penalty function values to rectify the ratio of predicted reduction and the actual reduction. Compared with the existing nonmonotone trust region methods, our method is independent of the nonmonotone parameter. We establish the global convergence of the proposed algorithm and give the numerical tests to show the efficiency of the algorithm.

scholarly journals An Improved Nonmonotone Filter Trust Region Method for Equality Constrained Optimization

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Zhong Jin
Keyword(s):  
Global Convergence ◽  
Constrained Optimization ◽  
Trust Region Method ◽  
Trust Region ◽  
Numerical Results ◽  
Trust Region Algorithm ◽  
Filter Technique ◽  
Sqp Methods ◽  
Equality Constrained Optimization ◽  
Nonlinear Equality

Motivated by the method of Su and Pu (2009), we present an improved nonmonotone filter trust region algorithm for solving nonlinear equality constrained optimization. In our algorithm a modified nonmonotone filter technique is proposed and the restoration phase is not needed. At every iteration, in common with the composite-step SQP methods, the step is viewed as the sum of two distinct components, a quasinormal step and a tangential step. A more relaxed accepted condition for trial step is given and a crucial criterion is weakened. Under some suitable conditions, the global convergence is established. In the end, numerical results show our method is effective.

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