Novel frameworks for auctions and optimization

This thesis contains two parts. Part I introduces novel frameworks for modeling uncertainty in auctions. This enables us to provide robust analysis to alternative specifications of preferences and information structures in Vickrey and VCG auctions. Part II introduces novel frameworks for understanding first-order methods in optimization. This enables us to (1) break 20-year barriers on the running time used for solving positive linear programs, (2) reduce the complexity for solving positive semidefinite programs, and (3) strengthen the theory of matrix multiplicative weight updates and improve the theory of linear-sized spectral sparsification.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2015

Author dc:creator

• Zhu, Zeyuan Allen

Advisor dc:contributor.advisor

• Jonathan A. Kelner and Silvio Micali.

• Electrical Engineering and Computer Science.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/101594

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/101594