Description

N&O seminar: Sophie Klumper (CWI)

Everyone is welcome to attend the next N&O seminar with Sophie Klumper with the title 'Budget Feasible Mechanisms for Procurement Auctions with Divisible Agents'.

The talk will take place in L017 at CWI, along with zoom support for remote participants. For more information and registration to get the Zoom link via e-mail, please contact Willem Feijen (willem.feijen at cwi.nl), Samarth Tiwari (samarth.tiwari at cwi.nl) or Sven Polak (sven.polak at cwi.nl).

Abstract:  We consider budget feasible mechanisms for procurement auctions with additive valuation functions. For the divisible case, where agents can be allocated fractionally, there exists an optimal mechanism with approximation guarantee e/(e-1) under the small bidder assumption. We study the divisible case without the small bidder assumption, but assume that the true costs of the agents are bounded by the budget. This setting lends itself to modeling economic situations in which the goods represent time and the agents' true costs are not necessarily small compared to the budget. Non-trivially, we give a mechanism with an approximation guarantee of 2.62, improving the optimal result of 3 for the indivisible case. Additionally, we give a lower bound on the approximation guarantee of 1.25. We then study the problem in more competitive markets and assume that the agents' value over cost efficiencies are bounded by some k. For k <= 2, we give a mechanism with an approximation guarantee of 2 and a lower bound of 1.18. Finally, we extend our results to different agent types with concave additive valuation functions.

(Joint work with Guido Schäfer)

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Workshop on Semidefinite and Polynomial Optimization (Semester Programme)

This workshop is dedicated to recent developments in semidefinite and polynomial optimization, and their applications in combinatorial and continuous optimization, discrete geometry and quantum information. The program (under construction) will consist of invited lectures by experts in the field. It will also feature lectures by younger researchers and ample time will be left for free discussions. 

This workshop is co-organized by Jop Briët and Monique Laurent.

Here you can find more information on the program of CWI's Semidefinite and Polynomial Optimization Workshop.

Please register here.

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Workshop on Solving Polynomial Equations and Applications (Semester Programme)

Polynomial equations are at the heart of many problems in pure and applied mathematics. They form a powerful tool for modelling nonlinear phenomena in the sciences. Application areas range from robotics, chemistry and computer vision to quantum physics and statistics. Recent progress has made it possible to reliably solve challenging polynomial equations arising in such practical contexts. This workshop will feature a friendly introduction to existing methods, presentations of the latest software tools and research talks by experts in the field. The focus will be on new trends and methodology, as well as applications in the sciences.

This workshop is co-organized by Monique Laurent and Simon Telen.

Here you can find more information on the program of CWI's Solving Polynomial Equations and Applications workshop.

Please register here.

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Workshop on Polynomial Optimization and Applications in Control and Energy (Semester Programme)

This workshop is devoted to the application of polynomial optimization methods in the analysis and control of dynamical systems and energy networks. The polynomial optimization approach offers a powerful framework to model hard nonconvex, nonlinear control problems as infinite dimensional linear optimization problems over measure spaces. The rich interplay between functional analysis and operator theory, and real algebraic geometry, underlies the nowadays well-known moment/sum-of-squares hierarchy of relaxations, that allows to efficiently obtain converging sequences of bounds. This approach has also been recently developed to attack large optimal power flow problems in large electrical networks. The program (under construction) will feature lectures by experts in the field and ample time will be left for discussions.

This workshop is co-organized by Monique Laurent and Bert Zwart.

Here you can find more information on the program of CWI's Polynomial Optimization and Applications in Control and Energy workshop.

Please register here.

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