Moment and polynomial optimization has received high attention in recent decades. It has
beautiful theory and efficient methods, as well as broad applications for various …

Within the frame of parametric design, in the present work we focus on a very special
objective, namely parametrically generating families of purely compressed shells. A similar …

This paper deals with an SOS-convex (sum of squares convex) polynomial optimization
problem with spectrahedral uncertain data in both the objective and constraints. By using a …

Non-convex optimization problems arise frequently in machine learning, including feature
selection, structured matrix learning, mixture modeling, and neural network training. We …

We present generalizations of Newton's method that incorporate derivatives of an arbitrary
order d but maintain a polynomial dependence on dimension in their cost per iteration. At …

We study a class of polynomial optimization problems with a robust polynomial matrix
inequality (PMI) constraint where the uncertainty set itself is also defined by a PMI. These …

We consider the problem of decomposing a multivariate polynomial as the difference of two
convex polynomials. We introduce algebraic techniques which reduce this task to linear …

We begin the study of one of the main themes of the book, namely, the relationships
between nonnegative polynomials, sums of squares, and semidefinite programming. The …

This textbook originates from a course for graduate students that I taught at Konstanz
University approximately five or six times over the past twenty years. While the first part of the …

In this article, a mathematical programming problem under affinely parameterized uncertain
data with multiple objective functions given by SOS-convex polynomials, denoting by (UMP) …