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

2016 ◽  
Vol 6 (2) ◽  
pp. 161-173 ◽  
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

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.

scholarly journals New Exact Penalty Functions for Nonlinear Constrained Optimization Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Bingzhuang Liu ◽  
Wenling Zhao
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Penalty Functions ◽  
Exact Penalty Functions ◽  
Local Minimizers ◽  
Constrained Optimization Problems ◽  
Nonlinear Constrained Optimization ◽  
Primal Problem ◽  
Mild Conditions ◽  
Constrained Problem

For two kinds of nonlinear constrained optimization problems, we propose two simple penalty functions, respectively, by augmenting the dimension of the primal problem with a variable that controls the weight of the penalty terms. Both of the penalty functions enjoy improved smoothness. Under mild conditions, it can be proved that our penalty functions are both exact in the sense that local minimizers of the associated penalty problem are precisely the local minimizers of the original constrained problem.

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.

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.

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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