One of the very important applications of auctions in many countries in last few years in financial domain has been privatization of state owned enterprises. Traditionally auction based mechanisms have been used for leasing of mining rights, bandwidth allocation etc. In last few years there has been growing interest in Internet based market places because of wide spread use of auction based protocols for electronic commerce. Many Internet based sites have implemented different types of auctions. In this paper we analyze the problem of Initial Public Offering (IPO) of Government owned companies. We also consider scenario with different types of constraints. We formulate this problem as nonlinear integer programming problem. An algorithm, which computes the optimum solution, has been developed. The algorithm generates optimum solution with polynomial time complexity.