Representando o vendedor e a sociedade : mecanismos com dois critérios para leilões combinatórios com demandas unitárias

This work focuses on obtaining truthful mechanisms that aim at maximizing both the revenue and the economic efficiency (social welfare) for the unitdemand combinatorial auction problem (UDCAP), in which a set of k items is auctioned to a set of n consumers. Although each consumer bids on all items, no consumer can purchase more than one item in the UDCAP. We present a framework for devising poly-time randomized competitive truthful mechanisms that can be used to either favor economic efficiency or revenue.

Multistep stochastic mirror descent for risk-averse convex stochastic programs based on extended polyhedral risk measures

We consider risk-averse convex stochastic programs expressed in terms of extended polyhedral risk measures. We derive computable con dence intervals on the optimal value of such stochastic programs using the Robust Stochastic Approximation and the Stochastic Mirror Descent (SMD) algorithms. When the objective functions are uniformly convex, we also propose a multistep extension of the Stochastic Mirror Descent algorithm and obtain con dence intervals on both the optimal values and optimal solutions. Numerical simulations show that our con dence intervals are much less conservative and are quicker to compute than previously obtained con dence intervals for SMD and that the multistep Stochastic Mirror Descent algorithm can obtain a good approximate solution much quicker than its nonmultistep counterpart. Our con dence intervals are also more reliable than asymptotic con dence intervals when the sample size is not much larger than the problem size.