sepa_minor.h
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30 * This separator detects all principal minors of the matrix \f$ xx' \f$ for which all auxiliary variables \f$ X \f$
31 * exist, i.e., two indices \f$ i \neq j \f$ such that \f$ X_{ii} \f$, \f$ X_{jj} \f$, and \f$ X_{ij} \f$ exist. Because
35 * A(x,X) = \begin{bmatrix} 1 & x_i & x_j \\ x_i & X_{ii} & X_{ij} \\ x_j & X_{ij} & X_{jj} \end{bmatrix}
38 * is also required to be positive semi-definite. Let \f$ v \f$ be a negative eigenvector for \f$ A(x^*,X^*) \f$ in a
39 * point \f$ (x^*,X^*) \f$, which implies that \f$ v' A(x^*,X^*) v < 0 \f$. To cut off \f$ (x^*,X^*) \f$, the separator
43 * To identify which entries of the matrix X exist, we (the separator) iterate over the available nonlinear constraints.
48 * Then, we go through the found bilinear terms \f$(yz)\f$ and if the corresponding \f$y^2\f$ and \f$z^2\f$ exist, then we have found
51 * For circle packing instances, the minor cuts are not really helpful (see [Packing circles in a square: a theoretical
52 * comparison of various convexification techniques](http://www.optimization-online.org/DB_HTML/2017/03/5911.html)).
53 * Furthermore, the performance was negatively affected, thus circle packing constraint are identified and ignored in
54 * the above algorithm. This behavior is controlled with the parameter "separating/minor/ignorepackingconss".
57 /*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/
Definition: struct_scip.h:68
Definition: objbenders.h:43
SCIP callable library.