E. Panier. On the need for special purpose algorithms for minimax eigenvalue problems. Journal Opt. Theory Appl., 62(2):279--287, August 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....case, the problem is in fact convex (but still nondifferentiable) Many researchers have considered this problem. Relevant work includes Cullum et al. [CDW75] Craven and Mond [CM81] Polak and Wardi [PW82] Fletcher [Fle85] Shapiro [Sha85] Friedland et al. FNO87] Goh and Teo [GT88] Panier [Pan89], Allwright [All89] Overton [Ove88, Ove92, OW93, OW92] Ringertz [Rin91] Fan and Nekooie [FN92] and Fan [Fan92] In [BY89] Boyd and Yang use the cutting plane algorithm and Shor s subgradient method [Sho85] to solve eigenvalue minimization problems that arise in control theory. They also ....

E. Panier. On the need for special purpose algorithms for minimax eigenvalue problems. Journal Opt. Theory Appl., 62(2):279--287, August 1989.

.... Wolkowicz [Wol81] and Kojima, Kojima and Hara [KKH94] Many researchers have worked on the problem of minimizing the maximum eigenvalue of a symmetric matrix, which can be cast as a semidefinite program (see x2) See, for instance, Cullum, Donath and Wolfe [CDW75] Goh and Teo [GT88] Panier [Pan89], Allwright [All89] Overton [Ove88, Ove92] Overton and Womersley [OW93, OW92] Ringertz [Rin91] Fan and Nekooie [FN92] Fan [Fan93] Hiriart Urruty and Ye [HUY95] Shapiro and Fan [SF94] and Pataki [Pat94] Interior point methods for LPs were introduced by Karmarkar in 1984 [Kar84] although ....

E. Panier. On the need for special purpose algorithms for minimax eigenvalue problems. Journal Opt. Theory Appl., 62(2):279--287, August 1989.

....1 and 2 , each a smooth function of x 2 2 . Thus standard minmax optimization techniques (e.g. MO80] cannot be applied. Suggestions 2 for transforming the problem into a standard nonlinear programming form by means of determinants have been made [GT88] but these methods perform poorly [Pan89] for other comments on the use of determinants, see [FNO87] In the example given above, the maximum eigenvalue is convex in x. This is true in general when A depends linearly on x, since the Rayleigh principle can be used to show that the maximum eigenvalue is a convex function of the matrix ....

E.R. Panier. On the need for special purpose algorithms for minimax eigenvalue problems. Technical report, Dept. of Elec. Eng., University of Maryland, 1989.

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E. Panier. On the need for special purpose algorithms for minimax eigenvalue problems. Journal Opt. Theory Appl., 62(2):279--287, August 1989.

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