We use the method of interlacing polynomials introduced in our previous article to prove two
theorems known to imply a positive solution to the Kadison–Singer problem. The first is …

Convexity is a simple and natural notion which can be traced back to Archimedes (circa 250
BC), in connection with his famous estimate of the value of π (by using inscribed and …

This book aims at developing a thorough understanding of the most general theory for
interior-point methods, a class of algorithms for convex optimization problems. The study of …

We introduce the class of strongly Rayleigh probability measures by means of geometric
properties of their generating polynomials that amount to the stability of the latter. This class …

This article describes the current state of the art of interior-point methods (IPMs) for convex,
conic, and general nonlinear optimization. We discuss the theory, outline the algorithms, and …

ITHACA, NEW YORK 14853-3801 Page 1 SCHOOL OF OPERATIONS RESEARCH AND
INDUSTRIAL ENGINEERING COLLEGE OF ENGINEERING CORNELL UNIVERSITY ITHACA …

During the last two decades, major developments in convex optimization were focusing on
conic programming, primarily, on linear, conic quadratic and semidefinite optimization …

THE LAX CONJECTURE IS TRUE Consider a polynomial p on Rn of degree d (the maximum
of the degrees of the monomials in the expansi Page 1 PROCEEDINGS OF THE AMERICAN …

We present an overview of the essential elements of semidefinite programming as a
computational tool for the analysis of systems and control problems. We make particular …

We study analyticity, differentiability, and semismoothness of Löwner's operator and spectral
functions under the framework of Euclidean Jordan algebras. In particular, we show that …