Exact penalty decomposition method for zero-norm minimization based on MPEC formulation (Q6486740)

The authors reformulate the zero-norm minimization problem NEWLINE\[NEWLINE \min_{x\in R^n}\{\|x\|_0:\|Ax-b\|\leq\delta\},NEWLINE\]NEWLINE where \(\|x\|_0:=\sum_{i=1}^n\mathrm{card}(x_i)\) with \(\mathrm{card}(x_i)=\begin{cases} 1&\text{if }x_i\neq0\\ 0&\text{otherwise}\end{cases}\) as an equivalent mathematical program with equilibrium constraints and establish that its penalty problem, induced by adding the complementarity constraint to the objective, is exact. Numerical comparisons indicate that the proposed method is very efficient.