Convex Cones, Sets, and FunctionsPrinceton University, Department of Mathematics, Logistics Research Project, 1953 - Convex bodies - 152 pages |
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affine space Ant1 Ap(C Ap(M arbitrary asymptotic cones bounded centroid closed convex cone closed convex functions closed convex set concave concave function condition conjugate function Consider contains converges convex hull convex set coordinates corollary definition Denote dependent with positive derivative dimension equation existence exterior extreme ray finite number fixed flat follows function f(x half-space Hence implies inequality intersection LELAND LELAND STANFORD Let f(x level sets LIBRARIES lim f(x linear combination linearly independent minimum n-tuple non-negative open convex set ORGANIZED 1891 plane plane at infinity point set points in common polyhedral positive semidefinite positively homogeneous problem Proposition prove quadratic form real numbers relative boundary point relative boundary ray relative interior point s-convex satisfying Section segment sequence solution space STANFORD JUNIOR statement subset subspace support function supporting hyperplane Suppose t₁ Theorem unit vectors z-axis zero ξε τεΩ