Half-space representation refers to a method of defining convex sets using linear inequalities. In this representation, a convex set can be expressed as the intersection of half-spaces, each defined by a linear inequality of the form $$a^T x \leq b$$, where $$a$$ is a vector of coefficients, $$x$$ is a point in the space, and $$b$$ is a scalar. This approach emphasizes the geometric interpretation of convex sets as regions formed by intersecting these half-spaces, which is crucial in understanding their properties and applications in optimization.
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