An SQP feasible descent algorithm for nonlinear inequality constrained optimization without strict complementarity
In this paper, a kind of nonlinear optimization problems with nonlinear inequality constraints are discussed, and a new SQP feasible descent algorithm for solving the problems is presented. At each iteration of the new algorithm, a convex quadratic program (QP) which always has feasible solution is...
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| Published in: | Computers & mathematics with applications (1987) Vol. 49; no. 2; pp. 223 - 238 |
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| Format: | Journal Article |
| Language: | English |
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2005
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| ISSN: | 0898-1221, 1873-7668 |
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| Abstract | In this paper, a kind of nonlinear optimization problems with nonlinear inequality constraints are discussed, and a new SQP feasible descent algorithm for solving the problems is presented. At each iteration of the new algorithm, a convex quadratic program (QP) which always has feasible solution is solved and a master direction is obtained, then, an improved (feasible descent) direction is yielded by updating the master direction with an explicit formula, and in order to avoid the Maratos effect, a height-order correction direction is computed by another explicit formula of the master direction and the improved direction. The new algorithm is proved to be globally convergent and superlinearly convergent under mild conditions without the strict complementarity. Furthermore, the quadratic convergence rate of the algorithm is obtained when the twice derivatives of the objective function and constrained functions are adopted. Finally, some numerical tests are reported. |
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| AbstractList | In this paper, a kind of nonlinear optimization problems with nonlinear inequality constraints are discussed, and a new SQP feasible descent algorithm for solving the problems is presented. At each iteration of the new algorithm, a convex quadratic program (QP) which always has feasible solution is solved and a master direction is obtained, then, an improved (feasible descent) direction is yielded by updating the master direction with an explicit formula, and in order to avoid the Maratos effect, a height-order correction direction is computed by another explicit formula of the master direction and the improved direction. The new algorithm is proved to be globally convergent and superlinearly convergent under mild conditions without the strict complementarity. Furthermore, the quadratic convergence rate of the algorithm is obtained when the twice derivatives of the objective function and constrained functions are adopted. Finally, some numerical tests are reported. |
| Author | Tang, Chun-Ming Jian, Jin-Bao |
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| Cites_doi | 10.1007/BF00940684 10.1007/BF01580880 10.1023/A:1022655423083 10.1007/BF01395810 10.1007/BF01580395 10.1007/BF02192227 10.1137/0728063 10.1007/BFb0120947 10.1007/BF01580879 10.1137/0325051 10.1137/0729072 10.1007/BF00932858 10.1137/0326046 10.1007/BF01581247 10.1007/s11766-000-0057-9 10.1007/s11766-997-0035-6 |
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| Keywords | Nonlinear Inequality Feasible Descent Algorithm SQP Superlinear Convergence Constrained Optimization |
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| SubjectTerms | Algorithms Constrained Optimization Constraints Descent Feasible Descent Algorithm Inequalities Mathematical analysis Mathematical models Nonlinear Inequality Nonlinearity Optimization SQP Superlinear Convergence |
| Title | An SQP feasible descent algorithm for nonlinear inequality constrained optimization without strict complementarity |
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