Wednesday, 15:15 - 15:40 h, Room: MA 042

 

Duan Li
MIQP solvers for quadratic programs with cardinality and minimum threshold constraints: A semidefinite program approach

Coauthors: Xiaoling Sun, Xiaojin Zheng

 

Abstract:
We consider in this research the cardinality constrained quadratic programming problem (P) that arise naturally in various real-world applications such as portfolio selection and subset selection in regression. We first investigate how to construct tighter semidefinite program (SDP) relaxation of the problem by applying a special Lagrangian decomposition scheme to the diagonal decomposition of the problem. We show that for any fixed diagonal decomposition, the dual problem can be reduced to a second-order cone program (SOCP), which
is the continuous relaxation of the perspective reformulation of
(P). This leads to an SDP formulation for computing the "best'' diagonal decomposition in the perspective reformulation. Numerical results comparing the performance of different MIQP reformulations of the problem show that the proposed SDP approach can help to improve the performance of the standard MIQP solvers for cardinality constrained quadratic programs.

 

Talk 1 of the contributed session Wed.3.MA 042
"Topics in mixed-integer nonlinear programming III" [...]
Cluster 14
"Mixed-integer nonlinear programming" [...]

 

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