Wednesday, 16:15 - 16:40 h, Room: MA 041

 

Hyemin Jeon
Convex quadratic programming with variable bounds

Coauthors: Jeffrey T. Linderoth, Andrew J. Miller

 

Abstract:
The set X= {(x,z,v) ∈ R+n × Bn × R+ | v ≥ xTQx,  xj ≤ zj  ∀ j } for some matrix Q \succeq 0
appears as substructure in many applications including portfolio management and data mining.
We aim to obtain a good approximation of \operatorname{conv}(X), and our approach starts by reformulating the set using Cholesky factorization Q = LLT.
In the reformulated set S = {(y,t,z,v) ∈ Rn × R+n × Bn × R+ |
v ≥ ∑jtj,  tj ≥ yj2  ∀ j,  0 ≤ [L-Ty]j ≤ zj  ∀ j }
,
the nonlinear constraints are convex and separable but the interaction between continuous and binary variables is more complicated.
Our work thus far has focused on studying the set S in the case n=2 denoted by S2.
A number of valid inequalities for S2 are derived, most of which are represented as second-order cone constraints.
Computational experiments are conducted to empirically compare the obtained relaxation to \operatorname{conv}(S2),
and to demonstrate how to utilize our valid inequalities for the case n>2.

 

Talk 3 of the invited session Wed.3.MA 041
"Quadratic integer programming" [...]
Cluster 14
"Mixed-integer nonlinear programming" [...]

 

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