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Numerical algorithms for nonlinear constrained optimization

Title
Numerical algorithms for nonlinear constrained optimization
Authors
정승은
Issue Date
1997
Department/Major
대학원 수학과
Keywords
Numerical algorithmsnonlinearoptimizationMathematics
Publisher
The Graduate School, Ewha Womans University
Degree
Master
Abstract
Nonlinear constrained problems can be solved numerically by the various methods. QR factorization is used in Newton and Partitioned QN methods to keep positive definiteness of the basis matrix. It is very expensive and does not have l-step superlinear convergence. We study an algorithm by Bigler-Nocedal-Schmid (BNS) which does not involve QR factorization and has 1-step superlinear convergence. We exhibit BNS method show superior computational results on the set of test problems with arbitrary starting values. Numerical results by BNS method are given and compared with Newton and Partitioned QN methods. ;비선형 제약 문제들은 여러 가지의 수치해석적 방법으로 근사해를 구할 수 있다. Newton과 Partitioned QN 방법은 QR-분해법을 사용하는데, 이것은 비용이 많이들며 또한 2 단계 초선형 수렴성을 가진다. 이 논문에서는 QR-분해법을 사용하지않고, 1 단계 초선형 수렴성을 가지는 BNS에 의한 방법을 제시하고, 기존의 방법들과 수치적 결과를 비교한다.
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