We show that the multiplicative weight update method provides a simple recipe for designing and analyzing optimal Bayesian Incentive Compatible (BIC) auctions, and reduces the time complexity of the problem to polynomial in parameters that depend on single agent instead of on the joint type space. We use this framework to design the first computationally efficient optimal auctions that satisfy ex-post Individual Rationality in the presence of constraints such as (hard, private) budgets and envy-freeness. Our techniques also yield first optimal auctions when buyers and a seller’s utility functions are non-linear. Scenarios with such functions include (a) auctions with “quitting rights”, (b) cost to borrow money beyond budget, (c) a seller’s and buyers’ risk aversion. We note, our framework easily yields optimal auctions for variety of auction settings considered in [Daskalakis and Weinberg 2012; Alaei et al. 2012; Cai et al. 2012a,b, 2013].