This chapter surveys how semidefinite programming can be used for finding good
approximative solutions to hard combinatorial optimization problems. The chapter begins …

Euclidean distance matrices (EDMs) are matrices of the squared distances between points.
The definition is deceivingly simple; thanks to their many useful properties, they have found …

Consider the problem of estimating the entries of a large matrix, when the observed entries
are noisy versions of a small random fraction of the original entries. This problem has …

Euclidean distance geometry is the study of Euclidean geometry based on the concept of
distance. This is useful in several applications where the input data consist of an incomplete …

This book is intended as a text covering the central concepts of practical optimization
techniques. It is designed for either self-study by professionals or classroom work at the …

Semidefinite programming (SDP) is a powerful framework from convex optimization that has
striking potential for data science applications. This paper develops a provably correct …

The matrix completion problem consists of finding or approximating a low-rank matrix based
on a few samples of this matrix. We propose a new algorithm for matrix completion that …

The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of
topics that show the spectrum of research, the richness of ideas, and the breadth of …

The Handbook of Linear Algebra provides comprehensive coverage of linear algebra
concepts, applications, and computational software packages in an easy-to-use handbook …

Convex Analysis is the calculus of inequalities while Convex Optimization is its application.
Analysis is inherently the domain of the mathematician while Optimization belongs to the …