116 citations · 1.1k across the 72 of their papers we have counts for
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Convergence Rates for Lasserre's Upper-Bound Hierarchy on with Gaussian Measure
Sander Gribling, Igor Klep, Poornendu Kumar
We establish quantitative convergence rates for Lasserre's measure-based upper-bound hierarchy on using the standard Gaussian measure as the reference measure. For a…
Upper bound hierarchies for noncommutative polynomial optimization
Igor Klep, Victor Magron, Gaël Massé +1
This work focuses on minimizing the eigenvalue of a noncommutative polynomial subject to a finite number of noncommutative polynomial inequality constraints. Based on the Helton-Mc…
Noncommutative Polynomial Optimization
Abhishek Bhardwaj, Igor Klep, Victor Magron
In this chapter we present the sums of Hermitian squares approach to noncommutative polynomial optimization problems. This is an extension of the sums of squares approach for polyn…
Sparse Noncommutative Polynomial Optimization
Igor Klep, Victor Magron, Janez Povh
This article focuses on optimization of polynomials in noncommuting variables, while taking into account sparsity in the input data. A converging hierarchy of semidefinite relaxati…
A Matrix Positivstellensatz with lifting polynomials
Igor Klep, Jiawang Nie
Given the projections of two semialgebraic sets defined by polynomial matrix inequalities, it is in general difficult to determine whether one is contained in the other. To address…
An exact duality theory for semidefinite programming based on sums of squares
Igor Klep, Markus Schweighofer
Farkas' lemma is a fundamental result from linear programming providing linear certificates for infeasibility of systems of linear inequalities. In semidefinite programming, such l…
Infeasibility certificates for linear matrix inequalities
Igor Klep, Markus Schweighofer
Farkas' lemma is a fundamental result from linear programming providing linear certificates for infeasibility of systems of linear inequalities. In semidefinite programming, such l…