Stationarity results for generating set search for linearly constrained optimization.

Technical Report · Wed Oct 01 00:00:00 EDT 2003

DOI:https://doi.org/10.2172/918255· OSTI ID:918255

Lewis, Robert Michael ^[1]; Torczon, Virginia Joanne ^[1]; Kolda, Tamara Gibson

---

1. College of William & Mary, Williamsburg, VA

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.

• Research Organization: Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC04-94AL85000
• OSTI ID: 918255
• Report Number(s): SAND2003-8550; TRN: US200818%%172
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
ALGORITHMS
CONVERGENCE
INFORMATION RETRIEVAL
CALCULATION METHODS