L0-Norm approximation
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\mathcal{L}_0-Norm Approximation
As already known, \mathcal{L}_0-norm functions do not possess continuity. To address this issue, it must be reformulated in an tractable manner. Within this study, we adopt the logarithmic \mathcal{L}_0-norm function as a means to effectively approximate discontinuous objective functions.
\|x\|_{0} = \lim \limits _{ \theta \rightarrow 0} \frac {\ln (1+\theta ^{-1} x)}{\ln (1+\theta ^{-1})},(x>0)
The norm \|x\|_{0} is defined as approximately equal to c multiplied by the natural logarithm of (1+\theta^{-1}x), where c is equal to $[1/\ln(1+\
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