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The purpose of this study is to verify the influence of internet usage frequency on women’s fertility intentions and to examine the mediating effects of gender role attitudes, under the influence of internet usage frequency that affects women’s fertility intentions, combined with the specific Chinese cultural context. A cross-sectional secondary data analysis was conducted using a sample of 3113 women of childbearing age in the Chinese General Social Survey in 2017 (CGSS2017). The results of the negative binomial regression model showed that, under the premise of controlling individual characteristic variables, the higher the frequency of internet usage, the lower the fertility intention (p < 0.01). The results of the mediating effect model show that the more frequently women use the internet, the lower their fertility intentions, and the less they agree with Chinese traditional gender roles, which are “men work outside to support the family while women stay at home to take care of the family”. These findings have implications in formulating public policies aimed at increasing the fertility rate; that is, it is not enough to increase women’s fertility intentions under China’s universal two-child policy. Moreover, public policy formulators need to consider gender role attitudes and the influence of the internet as a method for dissemination of information.

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This paper introduces a new exact and smooth penalty function to tackle constrained min-max problems. By using this new penalty function and adding just one extra variable, a constrained min-max problem is transformed into an unconstrained optimization one. It is proved that, under certain reasonable assumptions and when the penalty parameter is sufficiently large, the minimizer of this unconstrained optimization problem is equivalent to the minimizer of the original constrained one. Numerical results demonstrate that this penalty function method is an effective and promising approach for solving constrained finite min-max problems.