quadratic constrained quadratic programming MATLAB

[Yan]

Hello all,

I am trying to use Gurobi to solve my quadratic constrained quadratic programming problem. Code 'qptest2.m' is attached here. I am working on fedora19(64 bits), MATLAB 2012a, and Gurobi 5.5.

The objective function is quadratic with four variables, and one quadratic equality constraint. I ran the script with preloaded data 'test1.mat' (attached also), however it said
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Error using gurobi
Gurobi error 10020: Q matrix is not positive semi-definite (PSD)
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I check the Q matrix with svd to see the singular values, they all are positive, I have no idea why Gurobi think it's not PSD.

By the way, how to set the constraint to be quadratic only in the better way(using parameters), now I am setting A and b to be zero, and sense = '='.

Lastly, how to provide (do I need to provide) an initial guess (starting point) to the problem. If yes, how to do it.

Thanks a lot!

Yan

[Yan]

I noticed that my equality quadratic constrain matrix Qc is not positively semi-define (a1*a2+a3*a4=0).

[Jakob Sch.]

Hi Yan,

gurobi can only handle convex quadratic contraints of the form

• x'Qx + q'x <= b, where Q is Positive Semi-Definite (PSD)
• x'x <= y^2, where x is a vector of variables, and y is a non-negative variable (a Second-Order Cone)
• x'x <= y z, where x is a vector of variables, and y and z are non-negative variables (a rotated Second-Order Cone)

(see http://www.gurobi.com/documentation/5.5/reference-manual/node557). Equalityconstraint involving quadratic terms are not allowed (since they are not convex!).

Best regards,
Jakob

[BC]

Yan,

A quick comment that PSD requires all of your eigenvalues to be non-negative - the singular values are always non-negative by definition.

BC

[Yan]

To Jakob, unfortunately the quadratic constraint is not convex.

To BC, thank to the headup, I checked again the 'eig'.

Thanks a lot!!