On the Smoothing of the Square-Root Exact Penalty Function for Inequality Constrained Optimization

2006 ◽  
Vol 35 (3) ◽  
pp. 375-398 ◽  
Author(s):  
Zhiqing Meng ◽  
Chuangyin Dang ◽  
Xiaoqi Yang
Keyword(s):  
Constrained Optimization ◽  
Penalty Function ◽  
Exact Penalty Function ◽  
Exact Penalty ◽  
Square Root ◽  
Inequality Constrained Optimization

scholarly journals Smoothing Approximation to the Square-Root Exact Penalty Function

2016 ◽  
Vol 4 (1) ◽  
pp. 87-96
Author(s):  
Yaqiong Duan ◽  
Shujun Lian
Keyword(s):  
Penalty Function ◽  
Original Problem ◽  
Optimal Solution ◽  
Penalty Functions ◽  
Exact Penalty Functions ◽  
Exact Penalty ◽  
Square Root ◽  
Inequality Constrained Optimization ◽  
Numerical Examples ◽  
Mild Conditions

AbstractIn this paper, smoothing approximation to the square-root exact penalty functions is devised for inequality constrained optimization. It is shown that an approximately optimal solution of the smoothed penalty problem is an approximately optimal solution of the original problem. An algorithm based on the new smoothed penalty functions is proposed and shown to be convergent under mild conditions. Three numerical examples show that the algorithm is efficient.

scholarly journals Smoothing Approximation to the Square-Order Exact Penalty Functions for Constrained Optimization

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Shujun Lian ◽  
Jinli Han
Keyword(s):  
Constrained Optimization ◽  
Penalty Function ◽  
Original Problem ◽  
Optimal Solution ◽  
Penalty Functions ◽  
Exact Penalty Functions ◽  
Exact Penalty ◽  
Inequality Constrained Optimization ◽  
Numerical Examples ◽  
Mild Conditions

A method is proposed to smooth the square-order exact penalty function for inequality constrained optimization. It is shown that, under some conditions, an approximately optimal solution of the original problem can be obtained by searching an approximately optimal solution of the smoothed penalty problem. An algorithm based on the smoothed penalty functions is given. The algorithm is shown to be convergent under mild conditions. Two numerical examples show that the algorithm seems efficient.

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