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May 19, 2022. The paper A simplified treatment of Ramana’s exact dual for semidefinite programming ,
jointly written with B. Lourenco, was accepted at Optimization Letters.

Nov 26, 2021. I gave a talk at Workshop on Continuous Optimization and Related Topics .

Oct 5, 2021. I gave a talk on exponential size solutions in semidefinite programming at the Industrial Engineering Seminar at Lehigh University.

Aug 30, 2021. The paper An echelon form of weakly infeasible semidefinite programs and bad projections of the psd cone  
jointly written with A. Touzov, was accepted at Foundations of Computational Mathematics.

May 27, 2021. Alex Touzov won a 2nd prize (honorable mention) in the poster competition at the MIP 2021 workshop. The poster is
here. Congratulations, Alex!

May 11, 2021. I gave a talk on exponential size solutions in semidefinite programming at the the Fields Institute. The recording is

April 2, 2021. I gave a talk on exponential size solutions in semidefinite programming at the OR seminar at Carnegie Mellon University.
The most polished version of the talk is here .

March 1, 2021. We are excited about our new paper that we just posted: How do exponential size solutions arise in semidefinite programming?   G. Pataki, A. Touzov

Aug 6, 2020. Yuzixuan (Melody) Zhu defended her dissertation. Congratulations Melody!

Oct 17, 2019. I gave a talk at University of Chicago at the Colloquium in Computational and Applied Mathematics at the University of Chicago.

Feb 7, 2019. Our paper Sieve-SDP: a simple facial reduction algorithm to preprocess semidefinite programs by Y. Zhu, G. Pataki, Q. Tran-Dinh is now accepted at Mathematical Programming Computation. The paper is about a very simple preprocessing algorithm for SDPs, which works surprisingly well.

Jan 2, 2019. My paper Characterizing bad semidefinite programs: normal forms and short proofs
is now accepted at SIAM Review. This is a very short and easy-to-read characterization of pathological semidefinite systems, and I am excited that the proofs became so simple. In fact, the paper can be now read by an advanced undergraduate.

Dec 31, 2018. My paper On positive duality gaps in semidefinite programming   is now available. Positive gaps are quite a mysterious phenomenon in SDPs. This paper completely characterizes the 2 variable case and makes steps to understand positive gaps, when there are more than 2 variables.

Oct-Dec 2018: I am giving a talk at UCLA, the Naval Postgraduate School and the University of Goettingen. Later, in April 2019, I gave the same talk at the Simons Institute at Berkeley.

Nov 10, 2018. Come check out the Fall 2018 installment of the Triangle Lectures in Combinatorics . We have fantastic speakers.

Sept 28, 2018: Congratulations to Yuzixuan Zhu, who has received a first poster prize at the Princeton Day of Optimization . Her talk is here .

July 4 – 7, 2017. I am giving a talk at the Workshop on Modern Convex Optimization and Applications