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J. Oper. Res."],"published-print":{"date-parts":[[2024,10]]},"abstract":"<jats:p> In this paper, we consider the optimization problems with 0\/1-loss and sparsity constraints (0\/1-LSCO) that involve two blocks of variables. First, we define a [Formula: see text]-stationary point of 0\/1-LSCO, according to which we analyze the first-order necessary and sufficient optimality conditions. Based on these results, we then develop a gradient descent Newton pursuit algorithm (GDNP), and analyze its global and locally quadratic convergence under standard assumptions. 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