| In this short note we observe that results of Dennis and Audet extend naturally to a wide variety of deterministic sampling methods. For bound-constrained problems, we show that any method based on coordinate search which includes a sufficiently rich set of directions, for example random directions at each state of the sampling, will, when applied to Lipschitz continuous problems, have cluster points that satisfy generalized necessary conditions for optimality. The results also apply to the case of more general constraints, including so-called ``hidden'' or ``yes-no'' constraints. |
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