Successive Linearization Methods for Nonlinear Semidefinite Programs
We present a successive linearization method with a trust region-type globalization for the solution of nonlinear semidefinite programs. At each iteration, the method solves a quadratic semidefinite program, which can be converted to a linear semidefinite program with a second order cone constraint....
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| Published in: | Computational optimization and applications Vol. 31; no. 3; pp. 251 - 273 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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Springer Nature B.V
01.07.2005
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| ISSN: | 0926-6003, 1573-2894 |
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| Abstract | We present a successive linearization method with a trust region-type globalization for the solution of nonlinear semidefinite programs. At each iteration, the method solves a quadratic semidefinite program, which can be converted to a linear semidefinite program with a second order cone constraint. A subproblem of this kind can be solved quite efficiently by using some recent software for semidefinite and second-order cone programs. The method is shown to be globally convergent under certain assumptions. Numerical results on some nonlinear semidefinite programs including optimization problems with bilinear matrix inequalities are reported to illustrate the behaviour of the proposed method. |
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| AbstractList | We present a successive linearization method with a trust region-type globalization for the solution of nonlinear semidefinite programs. At each iteration, the method solves a quadratic semidefinite program, which can be converted to a linear semidefinite program with a second order cone constraint. A subproblem of this kind can be solved quite efficiently by using some recent software for semidefinite and second-order cone programs. The method is shown to be globally convergent under certain assumptions. Numerical results on some nonlinear semidefinite programs including optimization problems with bilinear matrix inequalities are reported to illustrate the behaviour of the proposed method. We present a successive linearization method with a trust region-type globalization for the solution of nonlinear semidefinite programs. At each iteration, the method solves a quadratic semidefinite program, which can be converted to a linear semidefinite program with a second order cone constraint. A subproblem of this kind can be solved quite efficiently by using some recent software for semidefinite and second-order cone programs. The method is shown to be globally convergent under certain assumptions. Numerical results on some nonlinear semidefinite programs including optimization problems with bilinear matrix inequalities are reported to illustrate the behaviour of the proposed method. [PUBLICATION ABSTRACT] |
| Author | Nagel, Christian Fukushima, Masao Kato, Hirokazu Kanzow, Christian |
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| Cites_doi | 10.1080/10556789908805764 10.1007/BF03167197 10.1109/ACC.1994.751863 10.1017/S0962492901000071 10.1007/s10107-002-0347-5 10.1080/10556789908805766 10.1023/A:1011562523132 10.1287/mnsc.28.10.1106 10.1137/S0363012999349553 10.1007/PL00011370 10.1023/A:1011224403708 10.1287/mnsc.7.4.379 10.1137/S0363012900373483 10.1007/978-0-387-35699-0_3 10.1287/mnsc.31.10.1312 10.1137/S1052623402417298 10.1080/1055678031000098773 |
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| DOI | 10.1007/s10589-005-3231-4 |
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| Title | Successive Linearization Methods for Nonlinear Semidefinite Programs |
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