Exact penalty functions in proximal bundle methods for constrained convex nondifferentiable minimization

1991 ◽  
Vol 52 (1-3) ◽  
pp. 285-302 ◽  
Author(s):  
Krzysztof C. Kiwiel
Keyword(s):  
Penalty Functions ◽  
Bundle Methods ◽  
Exact Penalty Functions ◽  
Exact Penalty ◽  
Proximal Bundle Methods ◽  
Nondifferentiable Minimization

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.

Characterizations for perturbed exact penalty functions

2005 ◽  
Vol 62 (1) ◽  
pp. 101-106 ◽  
Author(s):  
X.Q. Yang ◽  
D. Ralph
Keyword(s):  
Penalty Functions ◽  
Exact Penalty Functions ◽  
Exact Penalty
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