scholarly journals A new exact penalty function method for continuous inequality constrained optimization problems

2010 ◽  
Vol 6 (4) ◽  
pp. 895-910 ◽  
Author(s):  
Changjun Yu ◽  
◽  
Kok Lay Teo ◽  
Liansheng Zhang ◽  
Yanqin Bai ◽  
...  
Keyword(s):  
Constrained Optimization ◽  
Penalty Function ◽  
Function Method ◽  
Optimization Problems ◽  
Exact Penalty Function ◽  
Penalty Function Method ◽  
Exact Penalty ◽  
Constrained Optimization Problems ◽  
Inequality Constrained Optimization

THE l1 PENALTY FUNCTION METHOD FOR NONCONVEX DIFFERENTIABLE OPTIMIZATION PROBLEMS WITH INEQUALITY CONSTRAINTS

2010 ◽  
Vol 27 (05) ◽  
pp. 559-576 ◽  
Author(s):  
TADEUSZ ANTCZAK
Keyword(s):  
Penalty Function ◽  
Function Method ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Inequality Constraints ◽  
Exact Penalty Function ◽  
Mathematical Programming Problem ◽  
Penalty Function Method ◽  
Exact Penalty ◽  
Penalized Optimization

In this paper, some new results on the l1 exact penalty function method are presented. A simple optimality characterization is given for the nonconvex differentiable optimization problems with inequality constraints via the l1 exact penalty function method. The equivalence between sets of optimal solutions in the original mathematical programming problem and its associated exact penalized optimization problem is established under suitable r-invexity assumption. The penalty parameter is given, above which this equivalence holds. Furthermore, the equivalence between a saddle point in the considered nonconvex mathematical programming problem with inequality constraints and a minimizer in its penalized optimization problem with the l1 exact penalty function is also established.

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.

An Adaptive Penalty Function Method for Constrained Optimization with Evolutionary Programming

2000 ◽  
Vol 4 (2) ◽  
pp. 164-170 ◽  
Author(s):  
Xinghuo Yu ◽  
◽  
Baolin Wu
Keyword(s):  
Constrained Optimization ◽  
Penalty Function ◽  
Function Method ◽  
Optimization Problems ◽  
Evolutionary Programming ◽  
Benchmark Problems ◽  
Local Optimum ◽  
Penalty Function Method ◽  
Adaptive Penalty ◽  
Adaptive Penalty Function

In this paper, we propose a novel adaptive penalty function method for constrained optimization problems using the evolutionary programming technique. This method incorporates an adaptive tuning algorithm that adjusts the penalty parameters according to the population landscape so that it allows fast escape from a local optimum and quick convergence toward a global optimum. The method is simple and computationally effective in the sense that only very few penalty parameters are needed for tuning. Simulation results of five well-known benchmark problems are presented to show the performance of the proposed method.

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