Global Convergence of a Trust Region Algorithm for Nonlinear Inequality Constrained Optimization Problems

2004 ◽  
Vol 25 (5-6) ◽  
pp. 571-592
Author(s):  
Hongxia Yin ◽  
Jiye Han ◽  
Zhongwen Chen
Keyword(s):  
Global Convergence ◽  
Constrained Optimization ◽  
Optimization Problems ◽  
Trust Region ◽  
Constrained Optimization Problems ◽  
Inequality Constrained Optimization ◽  
Trust Region Algorithm ◽  
Nonlinear Inequality

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 A Globally Convergent Parallel SSLE Algorithm for Inequality Constrained Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Zhijun Luo ◽  
Lirong Wang
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Linear Equations ◽  
Coefficient Matrix ◽  
Descent Direction ◽  
Constrained Optimization Problems ◽  
Inequality Constrained Optimization ◽  
Globally Convergent ◽  
Variable Distribution ◽  
Systems Of Linear Equations

A new parallel variable distribution algorithm based on interior point SSLE algorithm is proposed for solving inequality constrained optimization problems under the condition that the constraints are block-separable by the technology of sequential system of linear equation. Each iteration of this algorithm only needs to solve three systems of linear equations with the same coefficient matrix to obtain the descent direction. Furthermore, under certain conditions, the global convergence is achieved.

Smoothing Approximation to the New Exact Penalty Function with Two Parameters

2021 ◽  
pp. 2140010
Author(s):  
Jing Qiu ◽  
Jiguo Yu ◽  
Shujun Lian
Keyword(s):  
Global Solution ◽  
Penalty Function ◽  
Original Problem ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Exact Penalty ◽  
Constrained Optimization Problems ◽  
Inequality Constrained Optimization ◽  
Nonlinear Inequality ◽  
Two Parameters

In this paper, we propose a new non-smooth penalty function with two parameters for nonlinear inequality constrained optimization problems. And we propose a twice continuously differentiable function which is smoothing approximation to the non-smooth penalty function and define the corresponding smoothed penalty problem. A global solution of the smoothed penalty problem is proved to be an approximation global solution of the non-smooth penalty problem. Based on the smoothed penalty function, we develop an algorithm and prove that the sequence generated by the algorithm can converge to the optimal solution of the original problem.

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