SDP Diagonalizations and Perspective Cuts for a Class of Nonseparable MIQP

Frangioni, Antonio and Gentile, Claudio (2006) SDP Diagonalizations and Perspective Cuts for a Class of Nonseparable MIQP. Technical Report del Dipartimento di Informatica . Università di Pisa, Pisa, IT.

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Abstract

Perspective cuts are a computationally effective family of valid inequalities, belonging to the general family of disjunctive cuts, for Mixed-Integer Convex NonLinear Programming problems with a specific structure. The required structure can be forced upon models that would not originally display it by decomposing the Hessian of the problem into the sum of two positive semidefinite matrices, a generic and a diagonal one, so that the latter is ''as large as possible''. We compare two ways for computing the diagonal matrix: an inexpensive approach requiring a minimum eigenvalue computation and a more costly procedure which require the solution of a SemiDefinite Programming problem. The latter dramatically outperforms the former at least upon instances of the Mean-Variance problem in portfolio optimization.

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