23 citations · 82 across the 21 of their papers we have counts for
23 papers
Strict complementarity in semidefinite programming, singularity degree, and the (dis)connection of forward and backward errors
Gábor Pataki
Strict complementarity of a primal-dual pair of optimal solutions is fundamental in the numerical analysis of semidefinite programs (SDPs). Strict complementarity drives the conver…
A combinatorial approach to Ramana's exact dual for semidefinite programming
Gabor Pataki
Thirty years ago, in a seminal paper Ramana derived an exact dual for Semidefinite Programming (SDP). Ramana's dual has the following remarkable features: i) it is an explicit, pol…
A Simplified Treatment of Ramana's Exact Dual for Semidefinite Programming
Bruno F. Lourenço, Gábor Pataki
In semidefinite programming the dual may fail to attain its optimal value and there could be a duality gap, i.e., the primal and dual optimal values may differ. In a striking paper…
An echelon form of weakly infeasible semidefinite programs and bad projections of the psd cone
Gábor Pataki, Aleksandr Touzov
A weakly infeasible semidefinite program (SDP) has no feasible solution, but it has approximate solutions whose constraint violation is arbitrarily small. These SDPs are ill-posed…
How do exponential size solutions arise in semidefinite programming?
Gábor Pataki, Aleksandr Touzov
A striking pathology of semidefinite programs (SDPs) is illustrated by a classical example of Khachiyan: feasible solutions in SDPs may need exponential space even to write down. S…
On Positive Duality Gaps in Semidefinite Programming
Gabor Pataki
We present a novel analysis of semidefinite programs (SDPs) with positive duality gaps, i.e. different optimal values in the primal and dual problems. These SDPs are extremely path…