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We consider the revenue maximization problem of a monopolist via anon-Myersonian approach that could generalize to multiple items and multiplebuyers. Although such an approach does not lead to any closed-form solution ofthe problem, it does provide some insights into this problem from differentangles. In particular, we consider both Bayesian (Bayesian Incentive Compatible+ Bayesian Individually Rational) and Dominant-Strategy (Dominant-StrategyIncentive Compatible + ex-post Individually Rational) implementations, whereall the buyers have additive valuations and quasi-linear utilities and all thevaluations are independent across buyers (not necessarily independent acrossitems).  The main technique of our approach is to formulate the problem as an LP(probably with exponential size) and apply primal-dual analysis. We observethat any optimal solution of the dual program naturally defines the virtualvalue functions for the primal revenue maximization problem in the sense thatany revenue-maximizing auction must be a virtual welfare maximizer (cf.Myerson's auction for a single item [Myerson, 1981]).  Based on this observation, we characterize a sufficient and necessarycondition for BIC = DSIC, i.e., the optimal revenue of Bayesian implementationsequals to the optimal revenue of dominant-strategy implementations (BRev =DRev). The condition is if and only if the optimal DSIC revenue DRev can beachieved by a DSIC and ex-post IR virtual welfare maximizer withbuyer-independent virtual value functions (buyer i's virtual value isindependent of other buyers' valuations). In light of the characterization, wefurther show that when all the valuations are i.i.d., it is further equivalentto that separate-selling is optimal. In particular, it respects one result fromthe recent breakthrough work on the exact optimal solutions in the multi-itemmulti-buyer setting by Yao [2016].

Generalizing Virtual Values to Multidimensional Auctions: a Non-Myersonian Approach