Historically, scalability has been a major challenge for the successful application of
semidefinite programming in fields such as machine learning, control, and robotics. In this …

Slater's condition–existence of a “strictly feasible solution”–is a common assumption in conic
optimization. Without strict feasibility, first-order optimality conditions may be meaningless …

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

This book is aimed at upper-level undergraduate students of mathematics and statistics, and
graduate students of industrial engineering. We assume that the readers are familiar with …

A conic optimization problem is a problem involving a constraint that the optimization
variable be in some closed convex cone. Prominent examples are linear programs (LP) …

Semidefinite programming (SDP) solvers are increasingly used as primitives in many
program verification tasks to synthesize and verify polynomial invariants for a variety of …

We study the separability problem in mixtures of Dicke states ie, the separability of the so-
called Diagonal Symmetric (DS) states. First, we show that separability in the case of DS in …

We establish connections between the facial reduction algorithm of Borwein and Wolkowicz
and the self-dual homogeneous model of Goldman and Tucker when applied to conic …

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 …

We provide a framework for obtaining error bounds for linear conic problems without
assuming constraint qualifications or regularity conditions. The key aspects of our approach …