66 citations · 187 across the 28 of their papers we have counts for
26 papers · 1 filter
Further analysis and extension of the higher-order Newton method of Ahmadi, Chaudhry, and Zhang
Lucas ter Voert, Etienne de Klerk
We extend a th-order Newton method for unconstrained optimization by Ahmadi, Chaudhry, and Zhang [Advances in Mathematics, 452:109808] to optimization with SOS-convex polynomial…
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…
On the convergence rate of the boosted Difference-of-Convex Algorithm (DCA)
Hadi Abbaszadehpeivasti, Etienne de Klerk, Adrien Taylor
The difference-of-convex algorithm (DCA) is a well-established nonlinear programming technique that solves successive convex optimization problems. These sub-problems are obtained…
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…
Least multivariate Chebyshev polynomials on diagonally determined sets
Mareike Dressler, Simon Foucart, Mioara Joldes +3
We consider a new multivariate generalization of the classical monic (univariate) Chebyshev polynomial that minimizes the uniform norm on the interval . Let be the…
Optimization-Aided Construction of Multivariate Chebyshev Polynomials
Mareike Dressler, Simon Foucart, Mioara Joldes +3
This article is concerned with an extension of univariate Chebyshev polynomials of the first kind to the multivariate setting, where one chases best approximants to specific monomi…
The link between -norm approximation and effective Positivstellensatze for the hypercube
Etienne de Klerk, Juan Vera Lizcano
The Schmüdgen's Positivstellensatz gives a certificate to verify positivity of a strictly positive polynomial on a compact, basic, semi-algebraic set $\mathbf{K} \subset \mathb…
A predictor-corrector algorithm for semidefinite programming that uses the factor width cone
Felix Kirschner, Etienne de Klerk
We propose an interior point method (IPM) for solving semidefinite programming problems (SDPs). The standard interior point algorithms used to solve SDPs work in the space of posit…
Convergence rate analysis of randomized and cyclic coordinate descent for convex optimization through semidefinite programming
Hadi Abbaszadehpeivasti, Etienne de Klerk, Moslem Zamani
In this paper, we study randomized and cyclic coordinate descent for convex unconstrained optimization problems. We improve the known convergence rates in some cases by using the n…
Convergence rate analysis of the gradient descent-ascent method for convex-concave saddle-point problems
Moslem Zamani, Hadi Abbaszadehpeivasti, Etienne de Klerk
In this paper, we study the gradient descent-ascent method for convex-concave saddle-point problems. We derive a new non-asymptotic global convergence rate in terms of distance to…
The exact worst-case convergence rate of the alternating direction method of multipliers
Moslem Zamani, Hadi Abbaszadehpeivasti, Etienne de Klerk
Recently, semidefinite programming performance estimation has been employed as a strong tool for the worst-case performance analysis of first order methods. In this paper, we deriv…
Conditions for linear convergence of the gradient method for non-convex optimization
Hadi Abbaszadehpeivasti, Etienne de Klerk, Moslem Zamani
In this paper, we derive a new linear convergence rate for the gradient method with fixed step lengths for non-convex smooth optimization problems satisfying the Polyak-Lojasiewicz…
Construction of multivariate polynomial approximation kernels via semidefinite programming
Felix Kirschner, Etienne de Klerk
In this paper we construct a hierarchy of multivariate polynomial approximation kernels via semidefinite programming. We give details on the implementation of the semidefinite prog…
Revisiting semidefinite programming approaches to options pricing: complexity and computational perspectives
Didier Henrion, Felix Kirschner, Etienne de Klerk +3
In this paper we consider the problem of finding bounds on the prices of options depending on multiple assets without assuming any underlying model on the price dynamics, but only…
On the rate of convergence of the Difference-of-Convex Algorithm (DCA)
Hadi Abbaszadehpeivasti, Etienne de Klerk, Moslem Zamani
In this paper, we study the convergence rate of the DCA (Difference-of-Convex Algorithm), also known as the convex-concave procedure, with two different termination criteria that a…
The exact worst-case convergence rate of the gradient method with fixed step lengths for L-smooth functions
Hadi Abbaszadehpeivasti, Etienne de Klerk, Moslem Zamani
In this paper, we study the convergence rate of the gradient (or steepest descent) method with fixed step lengths for finding a stationary point of an -smooth function. We estab…
Jordan symmetry reduction for conic optimization over the doubly nonnegative cone: theory and software
Daniel Brosch, Etienne de Klerk
A common computational approach for polynomial optimization problems (POPs) is to use (hierarchies of) semidefinite programming (SDP) relaxations. When the variables in the POP are…
Convergence analysis of a Lasserre hierarchy of upper bounds for polynomial minimization on the sphere
Etienne de Klerk, Monique Laurent
We study the convergence rate of a hierarchy of upper bounds for polynomial minimization problems, proposed by Lasserre [SIAM J. Optim. 21(3) (2011), pp. 864-885], for the special…
A survey of semidefinite programming approaches to the generalized problem of moments and their error analysis
Etienne de Klerk, Monique Laurent
The generalized problem of moments is a conic linear optimization problem over the convex cone of positive Borel measures with given support. It has a large variety of applications…
Distributionally robust optimization with polynomial densities: theory, models and algorithms
Etienne de Klerk, Daniel Kuhn, Krzysztof Postek
In distributionally robust optimization the probability distribution of the uncertain problem parameters is itself uncertain, and a fictitious adversary, e.g., nature, chooses the…
Improved convergence rates for Lasserre-type hierarchies of upper bounds for box-constrained polynomial optimization
Etienne de Klerk, Roxana Hess, Monique Laurent
We consider the problem of minimizing a given -variate polynomial over the hypercube . An idea introduced by Lasserre, is to find a probability distribution on $[-…
On the Turing model complexity of interior point methods for semidefinite programming
Etienne de Klerk, Frank Vallentin
It is known that one can solve semidefinite programs to within fixed accuracy in polynomial time using the ellipsoid method (under some assumptions). In this paper it is shown that…
Bound-constrained polynomial optimization using only elementary calculations
Etienne de Klerk, Jean Lasserre, Monique Laurent +1
We provide a monotone non increasing sequence of upper bounds () converging to the global minimum of a polynomial on simple sets like the unit hypercube. The no…
Convergence analysis for Lasserre's measure--based hierarchy of upper bounds for polynomial optimization
Etienne de Klerk, Monique Laurent, Zhao Sun
We consider the problem of minimizing a continuous function f over a compact set K. We analyze a hierarchy of upper bounds proposed by Lasserre in [SIAM J. Optim. 21(3) (2011), pp.…