Copositive matrices with nondecreasing off-diagonal entries admit a PSD plus nonnegative decomposition, which implies exactness of a natural relaxation for separable quadratic optimization over the simplex.
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Cubic surfaces are equipped with positive geometries in dimensions 2, 3, and 4 whose positive arrangements, combinatorial ranks, and canonical forms are explored.
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Copositive Matrices with Ordered Off-Diagonal Entries
Copositive matrices with nondecreasing off-diagonal entries admit a PSD plus nonnegative decomposition, which implies exactness of a natural relaxation for separable quadratic optimization over the simplex.
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Positive Geometries from Cubic Surfaces
Cubic surfaces are equipped with positive geometries in dimensions 2, 3, and 4 whose positive arrangements, combinatorial ranks, and canonical forms are explored.