A trust-region algorithm combining line search filter method with Lagrange merit function for nonlinear constrained optimization

This paper presents a trust-region algorithm which employs line search filter technique with Lagrange merit function for solving nonlinear equality constrained programming. At the current iteration, the general full trust-region subproblem is decomposed into a pair of trust-region subproblems in nor...

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Vydáno v:Applied mathematics and computation Ročník 247; s. 281 - 300
Hlavní autoři: Pei, Yonggang, Zhu, Detong
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 15.11.2014
Témata:
Algorithms
Constraints
Convergence
Filter method
Iterative methods
Lagrange function
Line search
Mathematical analysis
Mathematical models
Nonlinear programming
Nonlinearity
Searching
Trust-region method
Line search
Nonlinear programming
Trust-region method
Lagrange function
Filter method
Convergence
ISSN:0096-3003, 1873-5649
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Shrnutí:This paper presents a trust-region algorithm which employs line search filter technique with Lagrange merit function for solving nonlinear equality constrained programming. At the current iteration, the general full trust-region subproblem is decomposed into a pair of trust-region subproblems in normal and tangential subspaces. The trial step is given by solving these two trust-region subproblems. Then, different from traditional trust-region method in which the next iterate is determined by the ratio of the actual reduction to the predicted reduction, the step size is decided by interior backtracking line search together with filter method. Consequently, the expensive computation raised by resolving trust-region subproblem many times to determine a new iteration point in traditional trust-region method can be reduced. And the difficult decisions in regard to the choice of penalty parameters in the merit functions can be avoided by using filter technique. The new method retains the global convergence to the first-order critical points under some reasonable assumptions without using a merit function. Meanwhile, by using Lagrange function in the filter, the method can overcome Maratos effect without using second order correction step and hence the superlinear local convergence is achieved. The preliminary numerical results are reported to show effectiveness of the proposed algorithm.
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ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2014.09.003