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We study a nondifferentiable fractional programming problem as follows: subject to , where is a semiconnected subset in a locally convex topological vector space , , and , . If , , and , , are arc-directionally differentiable, semipreinvex maps with respect to a continuous map satisfying and , then the necessary and sufficient conditions for optimality of are established.
Interval censored (IC) failure time data are often observed in medical follow-up studies and clinical trials where subjects can only be followed periodically, and the failure time can only be known to lie in an interval. In this paper, we propose a weighted Wilcoxon-type rank test for the problem of comparing two IC samples. Under a very general sampling technique developed by Fay (1999), the mean and variance of the test statistics under the null hypothesis can be derived. Through simulation studies, we find that the performance of the proposed test is better than that of the two existing Wilcoxon-type rank tests proposed by Mantel (1967) and R. Peto and J. Peto (1972). The proposed test is illustrated by means of an example involving patients in AIDS cohort studies.