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In this paper, an active set sequential quadratic programming algorithm with nonmonotone line search for nonlinear minmax problems is presented. At each iteration of the proposed algorithm, a main search direction is obtained by solving a reduced quadratic program which always has a solution. In order to avoid the Maratos effect, a correction direction is yielded by solving the reduced system of linear equations. Under mild conditions without the strict complementarity, the global anddoi:10.1017/s0004972700039745 fatcat:nzm6etkhpbhhhmgf52qnzkyzly