8 papers
Squared polynomial approximation kernels for the hypercube: improved error bounds and implications for Lasserre hierarchies
Sander Gribling, Etienne de Klerk, Juan C. Vera
We propose a new family of polynomial approximation kernels for approximating nonnegative polynomials on the hypercube . Our Kernels produce polynomial sums-of-squares of…
Degree Bounds for Positivstellensätze of general semialgebraic sets
Olga Heijmans-Kuryatnikova, Juan C. Vera, Luis F. Zuluaga
Let denote the minimum of a polynomial over a (general) compact semialgebraic set . A standard way to approximate is via hierarc…
Lagrangian Reformulation for Nonconvex Optimization: Tailoring Problems to Specialized Solvers
Rodolfo A. Quintero, Juan C. Vera, Luis F. Zuluaga
In recent years, there has been a surge of interest in studying different ways to reformulate nonconvex optimization problems, especially those that involve binary variables. This…
Duality of Hoffman constants
Javier F. Pena, Juan C. Vera, Luis F. Zuluaga
We show that a suitable Slater condition implies a duality inequality between the Hoffman constants of the following feasibility problems: $$ \begin{array}{r} Ax-b \in S\\ x \in R…
Linear Convergence and Error Bounds for Optimization Without Strong Convexity
Kira van Treek, Javier F. Peña, Juan C. Vera +1
Many optimization algorithms$\unicode{x2013}$including gradient descent, proximal methods, and operator splitting techniques$\unicode{x2013}$can be formulated as fixed-point iterat…
Revisiting the convergence rate of the Lasserre hierarchy for polynomial optimization over the hypercube
Sander Gribling, Etienne de Klerk, Juan Vera
We revisit the problem of minimizing a given polynomial on the hypercube . Lasserre's hierarchy (also known as the moment- or sum-of-squares hierarchy) provides a seq…