Change of generalized indices of stationary solutions. to multiparametric optimization

We study the local change of the generalized index, which is a modification of the Morse index and the stationary index, for the multiparametric optimization. Under the Regular Value Condition, the change of the generalized index around a triplet (x,v,t) is locally bounded by the dimension of the parameter vector t, where x is a variable vector and v a vector of the Lagrange multiplier space. We also discuss the local change of the generalized index around a pair (x,t).

Authors and Affiliations

1. Department of Mathematics and Physics, National Defense Academy, 1-10-20, Hashirimizu, Yokosuka 239-8686, Japan, e-mail: shida@cc.nda.ac.jp, , , , , , JP

   Masayuki Shida

Received: March 27, 1998 / Accepted: January 29, 2000¶Published online April 20, 2000

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