Quasi-Newton Methods for Solving Nonlinear Programming Problems
In the present paper the problem of constrained equality optimization is reduced to sequential solving a series of problems of quadratic programming. The Hessian of the Lagrangian is approximated by a sequence of symmetric positive definite matrices. The matrix approximation is updated at every iter...
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| Format: | Article |
| Language: | English |
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Vladimir Andrunachievici Institute of Mathematics and Computer Science
1996-03-01
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| Series: | Computer Science Journal of Moldova |
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| Online Access: | http://www.math.md/nrofdownloads.php?file=/files/csjm/v3-n3/v3-n3-(pp263-277).pdf |
| Summary: | In the present paper the problem of constrained equality optimization is reduced to sequential solving a series of problems of quadratic programming. The Hessian of the Lagrangian is approximated by a sequence of symmetric positive definite matrices. The matrix approximation is updated at every iteration by a Gram- Schmidt modified algorithm. We establish that methods is locally convergent and the sequence {xk}converges to the solution a two-step superlinear rate. |
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| ISSN: | 1561-4042 |