This paper compares optimization models in the context of spectrum auctions as a valid mechanism for the resources allocation in telecommunications. Relaxation algorithms are designed to implement the auction. This approach maximizes the revenue, subject to interference and market constraints. The market is modeled on three different types of behavior, namely: normal, conservative and aggressive. In addition to the revenue, the paper presents the spectrum utilization and price as part of the results. It has been concluded that the spectrum allocation offers tools to the auctioneer and the bidder to make decisions driven at maximizing the revenue.