Quadratic minimisation problems in statistics - Albers, C.J.; Critchley, F.; Gower, J.C. (Journal of multivariate analysis, 2011)
We consider the problem min x ( x − t ) ′ A ( x − t ) subject to x ′ B x + 2 b ′ x = k where A is positive definite or positive semi-definite. Variants of this problem are discussed within the framework of a general unifying methodology. These include non-trivial considerations that arise when (i) A and/or B are not of full rank and (ii) t takes special forms (especially t = 0 which, under further conditions, reduces to the well-known two-sided eigenvalue solution). Special emphasis is placed on insights provided by geometrical interpretations.