We develop a practical semidefinite programming (SDP) facial reduction procedure that
utilizes computationally efficient approximations of the positive semidefinite cone. The …

The facial reduction algorithm (FRA) of Borwein and Wolkowicz and the extended dual of
Ramana provide a strong dual for the conic linear program P\sup\,{\, ⟨ c, x ⟩\, |\, Ax ≦ _ K …

In conic linear programming—in contrast to linear programming—the Lagrange dual is not
an exact dual: it may not attain its optimal value, or there may be a positive duality gap. The …

In this paper, we present a method for identifying infeasible, unbounded, and pathological
conic programs based on Douglas–Rachford splitting. When an optimization program is …

We introduce Sieve-SDP, a simple facial reduction algorithm to preprocess semidefinite
programs (SDPs). Sieve-SDP inspects the constraints of the problem to detect lack of strict …

Conic linear programs, among them semidefinite programs, often behave pathologically: the
optimal values of the primal and dual programs may differ, and may not be attained. We …

Despite the vast literature on DRS and ADMM, there has been very little work analyzing their
behavior under pathologies. Most analyses assume a primal solution exists, a dual solution …

This paper addresses the problem of distributed event localization using noisy range
measurements with respect to sensors with known positions. Event localization is …

In semidefinite programming (SDP), unlike in linear programming, Farkas' lemma may fail to
prove infeasibility. Here we obtain an exact, short certificate of infeasibility in SDP by an …

We suppose the existence of an oracle which solves any semidefinite programming (SDP)
problem satisfying strong feasibility (ie Slater's condition) simultaneously at its primal and …