Characterizing Optimal Adword Auctions

We present a number of models for the adword auctions used for pricing advertising slots on search engines such as Google, Yahoo! etc. We begin with a general problem formulation which allows the privately known valuation per click to be a function of both the identity of the advertiser and the slot. We present a compact characterization of the set of all deterministic incentive compatible direct mechanisms for this model. This new characterization allows us to conclude that there are incentive compatible mechanisms for this auction with a multi-dimensional type-space that are {\em not} affine maximizers. Next, we discuss two interesting special cases: slot independent valuation and slot independent valuation up to a privately known slot and zero thereafter. For both of these special cases, we characterize revenue maximizing and efficiency maximizing mechanisms and show that these mechanisms can be computed with a worst case computational complexity $O(n^2m^2)$ and $O(n^2m^3)$ respectively, where $n$ is number of bidders and $m$ is number of slots. Next, we characterize optimal rank based allocation rules and propose a new mechanism that we call the customized rank based allocation. We report the results of a numerical study that compare the revenue and efficiency of the proposed mechanisms. The numerical results suggest that customized rank-based allocation rule is significantly superior to the rank-based allocation rules.Comment: 29 pages, work was presented at a) Second Workshop on Sponsored Search Auctions, Ann Arbor, MI b) INFORMS Annual Meeting, Pittsburgh c) Decision Sciences Seminar, Fuqua School of Business, Duke Universit

Exponential penalty function control of loss networks

We introduce penalty-function-based admission control policies to approximately maximize the expected reward rate in a loss network. These control policies are easy to implement and perform well both in the transient period as well as in steady state. A major advantage of the penalty approach is that it avoids solving the associated dynamic program. However, a disadvantage of this approach is that it requires the capacity requested by individual requests to be sufficiently small compared to total available capacity. We first solve a related deterministic linear program (LP) and then translate an optimal solution of the LP into an admission control policy for the loss network via an exponential penalty function. We show that the penalty policy is a target-tracking policy--it performs well because the optimal solution of the LP is a good target. We demonstrate that the penalty approach can be extended to track arbitrarily defined target sets. Results from preliminary simulation studies are included.Comment: Published at http://dx.doi.org/10.1214/105051604000000936 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

A First-order Augmented Lagrangian Method for Compressed Sensing

We propose a first-order augmented Lagrangian algorithm (FAL) for solving the basis pursuit problem. FAL computes a solution to this problem by inexactly solving a sequence of L1-regularized least squares sub-problems. These sub-problems are solved using an infinite memory proximal gradient algorithm wherein each update reduces to "shrinkage" or constrained "shrinkage". We show that FAL converges to an optimal solution of the basis pursuit problem whenever the solution is unique, which is the case with very high probability for compressed sensing problems. We construct a parameter sequence such that the corresponding FAL iterates are eps-feasible and eps-optimal for all eps>0 within O(log(1/eps)) FAL iterations. Moreover, FAL requires at most O(1/eps) matrix-vector multiplications of the form Ax or A^Ty to compute an eps-feasible, eps-optimal solution. We show that FAL can be easily extended to solve the basis pursuit denoising problem when there is a non-trivial level of noise on the measurements. We report the results of numerical experiments comparing FAL with the state-of-the-art algorithms for both noisy and noiseless compressed sensing problems. A striking property of FAL that we observed in the numerical experiments with randomly generated instances when there is no measurement noise was that FAL always correctly identifies the support of the target signal without any thresholding or post-processing, for moderately small error tolerance values

Formulación de microesferas mucoadherentes de rosiglitazona maleato y su evaluación in vitro usando técnica de gelificación ionotrópica

Aim: The objective of the present study is to design and evaluate mucoadhesive microspheres for oralcontrolled release.Materials and Method: Rosiglitazone maleate microspheres with a coat consisting of alginate and a mucoadhesivepolymer sodium carboxymethylcellulose, carbopol 934P and hydroxypropylmethylcellulosewere prepared by an orifice-ionic gelation process. The microspheres were evaluated for FTIR studies,morphology, particle size, micromeritic properties, percentage entrapment efficiency, in-vitro wash-offtest and in-vitro release studies.Results: The resulting microspheres were spherical and free flowing. The percent entrapment efficiencywas 68.2 to 85.6%. The microspheres exhibited good mucoadhesive property in the in vitro wash-off test.Rosiglitazone release from these mucoadhesive microspheres was slow and extended over 12 h durationof time depending on the composition of coat.Conclusions: The prepared mucoadhesive microspheres are thus suitable for oral controlled release ofRosiglitazone maleate and thereby help in the management of type II diabetes mellitus.Objetivo. El objetivo del presente estudio es diseñar y evaluar las microesferas mucoadherentes de liberacióncontrolada para uso oral.Material y métodos. Las microesferas de rosiglitazona maleato con una capa de alginato y polímerosmucoadherentes de carboximetilcelulosa de sodio, carbopol 934P e hidroxipropilmetilcelulosa fueronelaboradas por un proceso de gelificación iónica de orificio. Las microesferas se evaluaron medianterayos infrarrojos con transformado de Fourier, se estudio la morfología, el tamaño de partícula, las propiedades«micromeritics», el porcentaje de eficacia de entrapamiento, la prueba in vitro de «wash-off» yestudios in vitro de liberación.Resultados. Las microesferas que resultaban eran esféricas y de flujo libre. La eficiencia de captura fuede 68,2 a 85,6%. Las microesferas exhibieron buena propiedad mucoadherentes en el ensayo in vitro delavado. La liberación lde las microesferas mucoadherentes de Rosiglitazona fue lento y se prolongadomás de 12 h dependiendo de la composición de la capa.Conclusiones. Las microesferas preparadas con mucoadherentes son convenientes para la liberaciónoral controlada de rosiglitazona maleato y así ayudar en el tratamiento de la diabetes mellitus tipo II