Geodesic
Two-sided bounds of the smallest eigenvalue of a positive-definite matrix in the presence of restrictions
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIV, Tome 268 (2000), pp. 181-184

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The problem of minimizing Rayleigh quotient in the presence of restrictions is considered. A method for constructing two-sided bounds of the smallest eigenvalue is suggested. 
@article{ZNSL_2000_268_a11,
     author = {G. V. Savinov},
     title = {Two-sided bounds of the smallest eigenvalue of a positive-definite matrix in the presence of restrictions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {181--184},
     publisher = {mathdoc},
     volume = {268},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_268_a11/}
}
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G. V. Savinov. Two-sided bounds of the smallest eigenvalue of a positive-definite matrix in the presence of restrictions. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIV, Tome 268 (2000), pp. 181-184. http://geodesic.mathdoc.fr/item/ZNSL_2000_268_a11/