Smoothing Approximation to the New Exact Penalty Function with Two Parameters

Jing Qiu, Jiguo Yu, Shujun Lian
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Abstract

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.
新的双参数精确惩罚函数的平滑逼近
本文针对非线性不等式约束优化问题,提出了一种新的双参数非光滑惩罚函数。提出了一种二阶连续可微函数,它是非光滑惩罚函数的光滑逼近,并定义了相应的光滑惩罚问题。证明了光滑惩罚问题的一个全局解是非光滑惩罚问题的一个近似全局解。在光滑罚函数的基础上,提出了一种算法,并证明了该算法生成的序列收敛于原问题的最优解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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