Smoothing Approximation to the Square-Root Exact Penalty Function

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.

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

Journal of Applied Mathematics ◽

10.1155/2013/568316 ◽

2013 ◽

Vol 2013 ◽

pp. 1-7 ◽

Cited By ~ 4

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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Smoothing Approximation to the New Exact Penalty Function with Two Parameters

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595921400108 ◽

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

Computational Optimization and Applications ◽

10.1007/s10589-006-8720-6 ◽

2006 ◽

Vol 35 (3) ◽

pp. 375-398 ◽

Cited By ~ 20

Author(s):

Zhiqing Meng ◽

Chuangyin Dang ◽

Xiaoqi Yang

Keyword(s):

Constrained Optimization ◽

Penalty Function ◽

Exact Penalty Function ◽

Exact Penalty ◽

Square Root ◽

Inequality Constrained Optimization

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A new smoothing approach to exact penalty functions for inequality constrained optimization problems

Numerical Algebra Control and Optimization ◽

10.3934/naco.2016006 ◽

2016 ◽

Vol 6 (2) ◽

pp. 161-173 ◽

Cited By ~ 1

Author(s):

Ahmet Sahiner ◽

Gulden Kapusuz ◽

Nurullah Yilmaz

Keyword(s):

Constrained Optimization ◽

Optimization Problems ◽

Penalty Functions ◽

Exact Penalty Functions ◽

Exact Penalty ◽

Constrained Optimization Problems ◽

Inequality Constrained Optimization

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A Smoothing Method of the Square-root Exact Penalty Function for Inequality Constrained Optimization

2010 Third International Joint Conference on Computational Science and Optimization ◽

10.1109/cso.2010.156 ◽

2010 ◽

Author(s):

Sanming Liu ◽

Zhijie Wang ◽

Enmin Feng

Keyword(s):

Constrained Optimization ◽

Penalty Function ◽

Smoothing Method ◽

Exact Penalty Function ◽

Exact Penalty ◽

Square Root ◽

Inequality Constrained Optimization

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Perturbed smoothing approach to the lower order exact penalty functions for nonlinear inequality constrained optimization

Tamkang Journal of Mathematics ◽

10.5556/j.tkjm.50.2019.2625 ◽

2018 ◽

Vol 50 (1) ◽

pp. 37-60 ◽

Cited By ~ 1

Author(s):

Binh Thanh Nguyen ◽

Yanqin Bai ◽

Xin Yan ◽

Touna Yang

Keyword(s):

Constrained Optimization ◽

Nonlinear Optimization ◽

Penalty Function ◽

Lower Order ◽

Optimization Problem ◽

Inequality Constraints ◽

Penalty Functions ◽

Exact Penalty Functions ◽

Exact Penalty ◽

Nonlinear Inequality

In this paper, we propose two new smoothing approximation to the lower order exact penalty functions for nonlinear optimization problems with inequality constraints. Error estimations between smoothed penalty function and nonsmooth penalty function are investigated. By using these new smooth penalty functions, a nonlinear optimization problem with inequality constraints is converted into a sequence of minimizations of continuously differentiable function. Then based on each of the smoothed penalty functions, we develop an algorithm respectively to finding an approximate optimal solution of the original constrained optimization problem and prove the convergence of the proposed algorithms. The effectiveness of the smoothed penalty functions is illustrated through three examples, which show that the algorithm seems efficient.

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