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Nonnegative definite matrices and their applications to matrix quadratic programming problems. (English) Zbl 0764.15010

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.

MSC:

15B48 Positive matrices and their generalizations; cones of matrices
15A09 Theory of matrix inversion and generalized inverses
90C20 Quadratic programming
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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
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