New Sequential Quadratically-Constrained Quadratic Programming Method of Feasible Directions and Its Convergence Rate |
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Authors: | J B Jian |
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Institution: | (1) College of Mathematics and Informatics Science, Guangxi University, Nanning, China |
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Abstract: | This paper discusses optimization problems with nonlinear inequality constraints and presents a new sequential quadratically-constrained
quadratic programming (NSQCQP) method of feasible directions for solving such problems. At each iteration. the NSQCQP method
solves only one subproblem which consists of a convex quadratic objective function, convex quadratic equality constraints,
as well as a perturbation variable and yields a feasible direction of descent (improved direction). The following results
on the NSQCQP are obtained: the subproblem solved at each iteration is feasible and solvable: the NSQCQP is globally convergent
under the Mangasarian-Fromovitz constraint qualification (MFCQ); the improved direction can avoid the Maratos effect without
the assumption of strict complementarity; the NSQCQP is superlinearly and quasiquadratically convergent under some weak assumptions
without thestrict complementarity assumption and the linear independence constraint qualification (LICQ).
Research supported by the National Natural Science Foundation of China Project 10261001 and Guangxi Science Foundation Projects
0236001 and 0249003.
The author thanks two anonymous referees for valuable comments and suggestions on the original version of this paper. |
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Keywords: | Inequality constraints optimization quadratic constraints quadratic programming convergence rate |
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