Stationarity results for generating set search for linearly constrained optimization.

Lewis, Robert Michael (College of William & ; Mary, Williamsburg, VA) ; Torczon, Virginia Joanne (College of William & ; Mary, Williamsburg, VA) ; Kolda, Tamara Gibson

Sandia National Laboratories

关键词: 99 General And Miscellaneous//Mathematics, Computing, And Information Science;    Information Retrieval;    Calculation Methods;    Algorithms;    97;   

DOI  :  10.2172/918255
RP-ID  :  SAND2003-8550
RP-ID  :  AC04-94AL85000
RP-ID  :  918255

美国|英语

来源: UNT Digital Library

【 摘 要 】

We derive new stationarity results for derivative-free, generating set search methods for linearly constrained optimization. We show that a particular measure of stationarity is of the same order as the step length at an identifiable subset of the iterations. Thus, even in the absence of explicit knowledge of the derivatives of the objective function, we still have information about stationarity. These results help both unify the convergence analysis of several classes of direct search algorithms and clarify the fundamental geometrical ideas that underlie them. In addition, these results validate a practical stopping criterion for such algorithms.