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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Bibliographic Details
Published in:Journal of applied mathematics & computing Vol. 71; no. 1; pp. 1309 - 1338
Main Authors: Zhang, Dongdong, Chen, Zhongwen
Format: Journal Article
Language:English
Published: Dordrecht Springer Nature B.V 01.02.2025
Subjects:
Algorithms
Convergence
Lagrange multiplier
Methods
Neighborhoods
Optimization
Quadratic programming
Semidefinite programming
ISSN:1598-5865, 1865-2085
Online Access:Get full text
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Summary: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.
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ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-024-02277-z