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.
SDP Diagonalizations and Perspective Cuts for a Class of Nonseparable MIQP
FRANGIONI, ANTONIO;
2007-01-01
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.File | Dimensione | Formato | |
---|---|---|---|
SDP4PC1.pdf
accesso aperto
Tipologia:
Documento in Post-print
Licenza:
Creative commons
Dimensione
245.8 kB
Formato
Adobe PDF
|
245.8 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.