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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| Published in: | Journal of applied mathematics & computing Vol. 71; no. 1; pp. 1309 - 1338 |
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Springer Nature B.V
01.02.2025
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| Abstract | 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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| AbstractList | 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. |
| Author | Zhang, Dongdong Chen, Zhongwen |
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| Cites_doi | 10.1007/s10957-006-9078-8 10.1142/S0217595918500094 10.1002/rnc.807 10.1007/978-3-319-04247-3 10.1023/A:1018665102534 10.1142/S0217595920400126 10.1007/s10107-015-0915-0 10.1007/s10114-014-3241-1 10.1007/978-1-4612-1394-9 10.3934/jimo.2023019 10.1137/S1052623499357945 10.1007/s10589-022-00402-x 10.1016/j.cam.2016.05.007 10.1137/S1052623498333731 10.1137/S0363012900373483 10.1007/s10107-011-0449-z 10.1007/s10107-007-0105-9 10.1137/S1052623402417298 10.48550/arXiv.2210.17169 10.1023/A:1008640419184 |
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| SubjectTerms | Algorithms Convergence Lagrange multiplier Methods Neighborhoods Optimization Quadratic programming Semidefinite programming |
| Title | Superlinear convergence of a stabilized SQP-type method for nonlinear semidefinite programming |
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