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The fight on HIV/AIDS globally is on increase everyday.  Many research activities are pioneered to put the scourge under control.  In the present paper an exposition is made on the need to fight HIV/AIDS is presented and the role which Operations Research experts can play to reinforce research on HIV/AIDS. The paper also considers a mathematical modeling problem arising from Operations Research. It is that of constructing most effective utility function for HIV drug using cost and efficacy analysis. The problem is a typical max min problem of the utility function and also exploited the Piyavskii’s algorithm for finding the most efficacious drug and used four minimization algorithms namely gradient, Newton’s, Conjugate gradient and quasi-Newton’s algorithms to find the most cost-effective drug.

Piyavskii’s algorithm
Conjugate gradient
mathematical modeling.
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