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

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 the strict complementarity assumption and the linear independence constraint qualification (LICQ). [ABSTRACT FROM AUTHOR]