New Sequential Quadratically-Constrained Quadratic Programming Method of Feasible Directions and Its Convergence Rate

J. B. Jian
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J. B. Jian: Guangxi University

Journal of Optimization Theory and Applications, 2006, vol. 129, issue 1, No 7, 109-130

Abstract: 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).

Keywords: Inequality constraints; optimization; quadratic constraints; quadratic programming; convergence rate (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10957-006-9042-7

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