Convex relaxations and MIQCQP reformulations for a class of cardinality-constrained portfolio selection problems

In this paper we investigate a class of cardinality-constrained portfolio selection problems. We construct convex relaxations for this class of optimization problems via a new Lagrangian decomposition scheme. We show that the dual problem can be reduced to a second-order cone program problem which i...

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Bibliographic Details
Published in:Journal of global optimization Vol. 56; no. 4; pp. 1409 - 1423
Main Authors: Cui, X. T., Zheng, X. J., Zhu, S. S., Sun, X. L.
Format: Journal Article
Language:English
Published: Boston Springer US 01.08.2013
Springer
Springer Nature B.V
Subjects:
Analysis
Computation
Computer Science
Decomposition
Expected values
Investment analysis
Linear programming
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Portfolio management
Real Functions
Semidefinite programming
Studies
Mixed 0–1 QCQP reformulation
Second-order cone program
Semidefinite program
Portfolio selection
Cardinality constraint
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:In this paper we investigate a class of cardinality-constrained portfolio selection problems. We construct convex relaxations for this class of optimization problems via a new Lagrangian decomposition scheme. We show that the dual problem can be reduced to a second-order cone program problem which is tighter than the continuous relaxation of the standard mixed integer quadratically constrained quadratic program (MIQCQP) reformulation. We then propose a new MIQCQP reformulation which is more efficient than the standard MIQCQP reformulation in terms of the tightness of the continuous relaxations. Computational results are reported to demonstrate the tightness of the SOCP relaxation and the effectiveness of the new MIQCQP reformulation.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-012-9842-2