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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Veröffentlicht in:Computers & mathematics with applications (1987) Jg. 49; H. 2; S. 223 - 238
Hauptverfasser: Jian, Jin-Bao, Tang, Chun-Ming
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 2005
Schlagworte:
Algorithms
Constrained Optimization
Constraints
Descent
Feasible Descent Algorithm
Inequalities
Mathematical analysis
Mathematical models
Nonlinear Inequality
Nonlinearity
Optimization
SQP
Superlinear Convergence
Nonlinear Inequality
Feasible Descent Algorithm
SQP
Superlinear Convergence
Constrained Optimization
ISSN:0898-1221, 1873-7668
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-2
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ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2004.09.004