Inexact sequential quadratically constrained quadratic programming methods with nonmonotone line searches for convex programming

In this paper, we present inexact sequential quadratically constrained quadratic programming (SQCQP) methods with nonmonotone line searches for the convex programming problem. Kato, Narushima and Yabe proposed the SQCQP method whose subproblem is solved inexactly. Their inexact SQCQP method uses a monotone line search strategy. To reduce the number of merit function evaluations and to accept the unit step size easier, we apply the nonmonotone line search to their inexact SQCQP method. We present the algorithms of the inexact SQCQP method with the nonmonotone line searches and prove their global and superlinear convergence properties. Moreover, we give some numerical experiments to investigate the numerical performance of our proposed methods. AMS 2010 Mathematics Subject Classification. 65K05 90C30 90C55.