Discovering the conditions under which an optimization algorithm or search heuristic will
succeed or fail is critical for understanding the strengths and weaknesses of different …

When SIAM asked us to prepare a new edition of this book after less than three years from
publication, we expected a light duty. Just the correction of some typos and imprecisions …

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 quadratic assignment problem (QAP), one of the most difficult problems in the NP-hard
class, models many real-life problems in several areas such as facilities location, parallel …

We present an alternating direction dual augmented Lagrangian method for solving
semidefinite programming (SDP) problems in standard form. At each iteration, our basic …

We consider a Newton-CG augmented Lagrangian method for solving semidefinite
programming (SDP) problems from the perspective of approximate semismooth Newton …

In this paper, we consider the monotone inclusion problem consisting of the sum of a
continuous monotone map and a point-to-set maximal monotone operator with a separable …

This tutorial presents a theory of valid inequalities for mixed integer linear sets. It introduces
the necessary tools from polyhedral theory and gives a geometric understanding of several …

There exist efficient algorithms to project a point onto the intersection of a convex conic and
an affine subspace. Those conic projections are in turn the work-horse of a range of …

Existing global optimization techniques for nonconvex quadratic programming (QP) branch
by recursively partitioning the convex feasible set and thus generate an infinite number of …