Superlinear convergence of a stabilized SQP-type method for nonlinear semidefinite programming

The stabilized sequential quadratic programming (SQP) method can effectively deal with degenerate nonlinear optimization problems. In the case of nonunique Lagrange multipliers associated with a stationary point of an optimization problem, the stabilized SQP method still obtains superlinear and/or q...

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Vydáno v:Journal of applied mathematics & computing Ročník 71; číslo 1; s. 1309 - 1338
Hlavní autoři: Zhang, Dongdong, Chen, Zhongwen
Médium: Journal Article
Jazyk:angličtina
Vydáno: Dordrecht Springer Nature B.V 01.02.2025
Témata:
Algorithms
Convergence
Lagrange multiplier
Methods
Neighborhoods
Optimization
Quadratic programming
Semidefinite programming
ISSN:1598-5865, 1865-2085
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Shrnutí:The stabilized sequential quadratic programming (SQP) method can effectively deal with degenerate nonlinear optimization problems. In the case of nonunique Lagrange multipliers associated with a stationary point of an optimization problem, the stabilized SQP method still obtains superlinear and/or quadratic convergence to a primal-dual solution. In this paper, we propose a stabilized sequential quadratic semidefinite programming method for degenerate nonlinear semidefinite programming problems. Under the local error bound condition, the strict complementarity condition, and the second-order sufficient condition, we establish superlinear and/or quadratic convergence of the proposed method.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-024-02277-z