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Inequality constrained statistical problems have been extensively studied and widely applied.Here we review the main results and report the progress in our recent research and show how these results can be applied to environmental statis tical problems and medicine problems.The main contents are: 1.Mathematical programming approach to inequality constrained statistical problems; 2.Making statistical inference for inequality constrained problems; 3.Inequality constrained statistical problems in environmetrics and medical statistics a.Dose-response prob lems b.Problems with longitudinal data.