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Algorithmic problems on convex sets
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<p>Many problems in <a href="/facts/Mathematical_programming/oRn8Iv5I">mathematical programming</a> can be formulated as problems on <a href="/facts/Convex_set/vdAuJRJl">convex sets</a> or <a href="/facts/Convex_body/90knDx0u">convex bodies</a>. Six kinds of problems are particularly important:: Sec.2 optimization, violation, validity, separation, membership and emptiness. Each of these problems has a strong (exact) variant, and a weak (approximate) variant. </p><p>In all problem descriptions, <i>K</i> denotes a <a href="/facts/Compact_set/d0cgXJH7">compact</a> and <a href="/facts/Convex_set/vdAuJRJl">convex set</a> in R<i>n</i>. </p>