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Title: Nonlinearly-constrained optimization using asynchronous parallel generating set search.

Nonlinearly-constrained optimization using asynchronous parallel generating set search. Many optimization problems in computational science and engineering (CS&E) are characterized by expensive objective and/or constraint function evaluations paired with a lack of derivative information. Direct search methods such as generating set search (GSS) are well understood and efficient for derivative-free optimization of unconstrained and linearly-constrained problems. This paper addresses the more difficult problem of general nonlinear programming where derivatives for objective or constraint functions are unavailable, which is the case for many CS&E applications. We focus on penalty methods that use GSS to solve the linearly-constrained problems, comparing different penalty functions. A classical choice for penalizing constraint violations is {ell}{sub 2}{sup 2}, the squared {ell}{sub 2} norm, which has advantages for derivative-based optimization methods. In our numerical tests, however, we show that exact penalty functions based on the {ell}{sub 1}, {ell}{sub 2}, and {ell}{sub {infinity}} norms converge to good approximate solutions more quickly and thus are attractive alternatives. Unfortunately, exact penalty functions are discontinuous and consequently introduce theoretical problems that degrade the final solution accuracy, so we also consider smoothed variants. Smoothed-exact penalty functions are theoretically attractive because they retain the differentiability of the original problem. Numerically, they are a compromise between exact and {ell}{sub 2}{sup 2}, i.e., they more » converge to a good solution somewhat quickly without sacrificing much solution accuracy. Moreover, the smoothing is parameterized and can potentially be adjusted to balance the two considerations. Since many CS&E optimization problems are characterized by expensive function evaluations, reducing the number of function evaluations is paramount, and the results of this paper show that exact and smoothed-exact penalty functions are well-suited to this task. « less
Authors: ;
Publication Date:
OSTI Identifier:909393
Report Number(s):SAND2007-3257
TRN: US200722%%1088
DOE Contract Number:AC04-94AL85000
Resource Type:Technical Report
Data Type:
Research Org:Sandia National Laboratories
Sponsoring Org:USDOE
Country of Publication:United States
Language:English
Subject: 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; NONLINEAR PROGRAMMING; OPTIMIZATION; CALCULATION METHODS; NONLINEAR PROBLEMS; CONVERGENCE Nonlinear programming.; Optimization methods; Mathematical optimization.; Optimization.