Lewis, A. S. (1996). Derivatives of spectral functions. Mathematics of Operations Research, 21:576-588. Home/Search Document Details and Download
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Derivatives Of Orbital Functions, An Extension Of.. - Tam, Hill (Correct)
....one, it provides a totally new look to Lidskii s theorem. Inspired by Lewis approach a generalization of BerezinGel fand s result is given via nonsmooth analysis in Section 4. In order to carry out the approach, the derivatives of some orbital functions are studied and a number of results in [21] are generalized in Section 3. Then we determine the distance between a G orbit or its convex hull and a given point as applications in Section 5. The following is a framework for the extension which only requires basic knowledge of linear algebra. Let G be a closed subgroup of the orthogonal ....
....# W . Similarly we can define G invariant sets and functions. In other words, a H invariant (G invariant) function is constant on each orbit Hz (Gz) of z # W (z # V ) Thus we sometimes call it an orbital function. The results in this section generalize the corresponding indicated results in [21, 28]. Lemma 3.1. Compare [28, Lemma 3.2] Let # F such that ( #m ) # = 0, #m # #. Then max ( x) x # conv H#m = #m ) and arg max ( x) x # conv H#m = #m . 5 Proof. Notice that max ( x) x # conv H#m = max ( x) x # H#m = #m ) by (A2) since , #m ....
A.S. Lewis, Derivatives of spectral functions,Math. Oper. Res., 21:576--588, 1996.
Semidefinite and Lagrangian Relaxations for Hard Combinatorial.. - Wolkowicz (1999) (Correct)
....for LP can be extended to SDP. This was studied as early as 1948 by Bohnenblust [14] and later by Tausky [95] and also Barker and Carlson [9] More recently, motivated by the high interest in SDP, many new results on differentiability and multiplicity of eigenvalues have appeared, see e.g. Lewis [54, 55] and Pataki [73, 74] respectively. In addition, results on characterizing different types of homogeneous and self scaled cones appears in [34, 98, 36] Let P denote the cone of positive semidefinite matrices. Some sample results similar to LP are: the SDP cone is self polar, i.e. P = P : ....
A. S. LEWIS. Derivatives of spectral functions. Math. Oper. Res., 21(3):576-- 588, 1996.
Extensions of Classical Multidimensional Scaling: Computational.. - Trosset (Correct)
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Lewis, A. S. (1996). Derivatives of spectral functions. Mathematics of Operations Research, 21:576-588.
Digital Object Identifier (DOI) 10.1007/s101070100225 - Math Program Ser (Correct)
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Lewis, A.S. (1996): Derivatives of spectral functions. Math. Oper. Res. 21, 576--588
Semidefinite and Cone Programming Bibliography/Comments - Wolkowicz (2004) (Correct)
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A.S. LEWIS. Derivatives of spectral functions. Math. Oper. Res., 21(3):576--588, 1996. 46
Generalizations Of Ky Fan's Dominance Theorem And Some.. - Charles Dolberry Tin-Yau (Correct)
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A.S. Lewis, Derivatives of spectral functions, Math. Oper. Res., 21:576--588, 1996.
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