Chen, Yonglin Nonnegative definite matrices and their applications to matrix quadratic programming problems. (English) Zbl 0764.15010 Linear Multilinear Algebra 33, No. 3-4, 189-201 (1993). This paper examines relationships between the concept of a matrix being nonnegative definite over a subspace, generalized inverses, and matrix quadratic programming. An application is given to the common penalty method for handling constrained minimization. Reviewer: S.L.Campbell (Raleigh) Cited in 7 Documents MSC: 15B48 Positive matrices and their generalizations; cones of matrices 15A09 Theory of matrix inversion and generalized inverses 90C20 Quadratic programming Keywords:nonnegative definite matrices; generalized inverses; matrix quadratic programming; penalty method; constrained minimization PDFBibTeX XMLCite \textit{Y. Chen}, Linear Multilinear Algebra 33, No. 3--4, 189--201 (1993; Zbl 0764.15010) Full Text: DOI References: [1] Luenberger D., Linear and Nonlinear Programming (1989) [2] Fletcher R., Practical Methods of Optimization (1987) · Zbl 0905.65002 [3] DOI: 10.1137/1033001 · Zbl 0734.90062 · doi:10.1137/1033001 [4] Ben-Israel A., Generalized Inverses: Theory and Applications (1974) [5] Campbell S. L., Generalized Inverses of Linear Transformations (1979) · Zbl 0417.15002 [6] DOI: 10.1016/0024-3795(90)90007-Y · Zbl 0703.15006 · doi:10.1016/0024-3795(90)90007-Y [7] DOI: 10.1137/0703049 · Zbl 0147.13105 · doi:10.1137/0703049 [8] DOI: 10.1137/0117041 · Zbl 0265.15002 · doi:10.1137/0117041 [9] DOI: 10.1016/0022-247X(71)90072-2 · Zbl 0221.15014 · doi:10.1016/0022-247X(71)90072-2 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.