E. Polak and Y. Wardi. A nondi#erentiable optimization algorithm for the design of control systems subject to singular value inequalities over a frequency range. Automatica, 18(3):267--283, 1982.  Home/Search   Document Not in Database   Summary   Related Articles

....we have the standard conclusion that there exists a descent direction at a if and only if ##(a) and indeed in this case we may take as explicit descent direction the negative of the element of ##(a) of least norm. In particular we have: A is SSLS if and only if 0 ##(0) Polak and Wardi [PW82] have shown that for our particular #, ##(a) Co # #g i = z U Q i Uz, z , z z = 1 . 62) In particular if u is any unit eigenvector of (58) corresponding to the maximum eigenvalue #(a) of the matrix (58) then g i = u Q i u yields g ##(a) So it is very easy to ....

E. Polak and Y. Wardi. A nondi#erentiable optimization algorithm for the design of control systems subject to singular value inequalities over a frequency range. Automatica, 18(3):267--283, 1982.

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