On the Global Convergence of a Projective Trust Region Algorithm for Nonlinear Equality Constrained Optimization

A trust-region sequential quadratic programming (SQP) method is developed and analyzed for the solution of smooth equality constrained optimization problems. The trust-region SQP algorithm is based on filter line search technique and a composite-step approach, which decomposes the overall step as su...

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Bibliographic Details
Published in:Acta mathematica Sinica. English series Vol. 34; no. 12; pp. 1804 - 1828
Main Authors: Pei, Yong Gang, Zhu, De Tong
Format: Journal Article
Language:English
Published: Beijing Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.12.2018
Springer Nature B.V
Subjects:
Algorithms
Constraints
Convergence
Mathematics
Mathematics and Statistics
Optimization
Optimization algorithms
Quadratic programming
65K05
90C30
Sequential quadratic programming
global convergence
90C55
trust-region
filter line search
projection
49M37
ISSN:1439-8516, 1439-7617
Online Access:Get full text
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Summary:A trust-region sequential quadratic programming (SQP) method is developed and analyzed for the solution of smooth equality constrained optimization problems. The trust-region SQP algorithm is based on filter line search technique and a composite-step approach, which decomposes the overall step as sum of a vertical step and a horizontal step. The algorithm includes critical modifications of horizontal step computation. One orthogonal projective matrix of the Jacobian of constraint functions is employed in trust-region subproblems. The orthogonal projection gives the null space of the transposition of the Jacobian of the constraint function. Theoretical analysis shows that the new algorithm retains the global convergence to the first-order critical points under rather general conditions. The preliminary numerical results are reported.
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ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-018-7063-4