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Extending a fundamental result for (indefinite) quadratic programs, thispaper shows that certain non-convex piecewise programs have only a finitenumber of directional stationary values, and thus, possess only finitely manylocally minimum values. We present various special cases of our main results,in particular, an application to a least-squares piecewise affine regressionproblem for which every directional stationary point is locally minimizing.

On the Finite Number of Directional Stationary Values of Piecewise Programs