Difference between revisions of "QpDefine"

Revision as of 06:42, 29 August 2010

QpDefine is used to define a quadratic optimization problem -- a problem containing a linear or quadratic objective, and linear or quadratic constraints. It has been superceded by DefineOptimization in Analytica 4.3.

Please see that Analytica Optimizer manual for Analytica 4.2 for a description of QpDefine.

Notes

When filling in a quadratic matrix, there are, in theory, multiple ways to specify the coefficients. For example, the quadratic expression:

x^2 + 4*x*y + 3*y^2

would be, in theory, represented identically using the lower-triangular Q matrix:

[ 1 0 ]
[ 4 3 ]

its upper-trangular transpose, the symmetric Q-matrix:

[ 1 2 ]
[ 2 3 ]

or any convex combination of these. However, the "SOCP Barrier" engine only interprets the matrix correctly when it is symmetric. It only looks at the upper-triangle, and assumes that the lower-triangle coefficients are the same. In Analytica 4.2 and earlier, QpDefine does not convert a non-symmetric Q into its symmetric counterpart internally for you, so it is important that you provide a symmetric Q matrix, not a lower-triangular one.

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+[[QpDefine]] is used to define a quadratic optimization problem -- a problem containing a linear or quadratic objective, and linear or quadratic constraints.  It has been superceded by [[DefineOptimization]] in Analytica 4.3.
+Please see that Analytica Optimizer manual for Analytica 4.2 for a description of [[QpDefine]].
+== Notes ==
+When filling in a quadratic matrix, there are, in theory, multiple ways to specify the coefficients.  For example, the quadratic expression:
+ x^2 + 4*x*y + 3*y^2
+would be, in theory, represented identically using the lower-triangular Q matrix:
+ [ 1 0 ]
+ [ 4 3 ]
+its upper-trangular transpose, the symmetric Q-matrix:
+ [ 1 2 ]
+ [ 2 3 ]
+or any convex combination of these.  However, the "SOCP Barrier" engine only interprets the matrix correctly when it is symmetric.  It only looks at the upper-triangle, and assumes that the lower-triangle coefficients are the same.   In Analytica 4.2 and earlier, [[QpDefine]] does not convert a non-symmetric Q into its symmetric counterpart internally for you, so it is important that you provide a symmetric Q matrix, not a lower-triangular one.