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2016

On the Turing model complexity of interior point methods for semidefinite programming

de Klerk, E. & Vallentin, F., Sep 2016, In : SIAM Journal on Optimization. 26, 3, p. 1944-1961

Research output: Contribution to journalArticleScientificpeer-review

Ellipsoid Method
Semidefinite Program
Diophantine Approximation
Model Complexity
Interior Point Method
2020

Solving sparse polynomial optimization problems with chordal structure using the sparse bounded-degree sum-of-squares hierarchy

de Klerk, E., Marandi, A. & Dahl, J., Mar 2020, In : Discrete Applied Mathematics. 275, p. 95-110

Research output: Contribution to journalArticleScientificpeer-review

Sparse Polynomials
Degree Sum
Sum of squares
Polynomials
Optimization Problem
2016

Computer-assisted proofs and semidefinite programming

de Klerk, E., May 2016, In : Optima: Mathematical Optimization Society Newsletter. 100, p. 11-11 1 p.

Research output: Contribution to journalBook/Film/Article reviewOther research output

2018
125 Downloads (Pure)

A numerical evaluation of the bounded degree sum-of-squares hierarchy of Lasserre, Toh, and Yang on the pooling problem

Marandi, A., Dahl, J. & de Klerk, E., Jun 2018, In : Annals of Operations Research. 265, 1, p. 67-92

Research output: Contribution to journalArticleScientificpeer-review

Open Access
File
Evaluation
Pooling
Lower bounds
Optimization problem
Programming
2017

On the convergence rate of grid search for polynomial optimization over the simplex

de Klerk, E., Laurent, M., Sun, Z. & Vera Lizcano, J., Mar 2017, In : Optimization Letters. 11, 3, p. 597-608

Research output: Contribution to journalArticleScientificpeer-review

Rate of Convergence
Grid
Polynomial
Optimization
Hypergeometric Distribution
2018
80 Downloads (Pure)

Comparison of Lasserre's measure-based bounds for polynomial optimization to bounds obtained by simulated annealing

de Klerk, E. & Laurent, M., Nov 2018, In : Mathematics of Operations Research. 43, 4, p. 1317-1325

Research output: Contribution to journalArticleScientificpeer-review

File
Simulated annealing
Simulated Annealing
Polynomials
Polynomial
Optimization
2020

Convergence analysis of a Lasserre hierarchy of upper bounds for polynomial minimization on the sphere

de Klerk, E. & Laurent, M., Jan 2020, In : Mathematical Programming .

Research output: Contribution to journalArticleScientificpeer-review

Open Access
Convergence Analysis
Rate of Convergence
Polynomials
Upper bound
Polynomial
2016

Improved Convergence Rates for Lasserre-type Hierarchies of Upper Bounds for Box-Constrained Polynomial Optimization

de Klerk, E., Laurent, M. & Hess, R., 16 Mar 2016, Ithaca: Cornell University Library, 21 p. (arXiv; vol. 1603.03329).

Research output: Working paperOther research output

Open Access

On the Worst-Case Complexity of the Gradient Method with Exact Line Search for Smooth Strongly Convex Functions

de Klerk, E., Glineur, F. & Taylor, A., 30 Jun 2016, Itacha: Cornell University Library, 10 p. (arXiv; vol. arXiv:1606.09365).

Research output: Working paperOther research output

Line Search
Gradient Method
Convex function
Gradient Descent Method
Gradient
2020
18 Downloads (Pure)

Worst-case examples for Lasserre's measure-based hierarchy for polynomial optimization on the hypercube

de Klerk, E. & Laurent, M., 2020, In : Mathematics of Operations Research. 45, 1, p. 86-98

Research output: Contribution to journalArticleScientificpeer-review

Open Access
File
Hypercube
Polynomials
Polynomial
Optimization
Convergence Rate
2017
87 Downloads (Pure)

On the worst-case complexity of the gradient method with exact line search for smooth strongly convex functions

de Klerk, E., Glineur, F. & Taylor, A., Oct 2017, In : Optimization Letters. 11, 7, p. 1185–1199 15 p.

Research output: Contribution to journalArticleScientificpeer-review

Open Access
File
Line Search
Gradient Method
Convex function
Gradient Descent Method
Gradient
2019
18 Downloads (Pure)

A survey of semidefinite programming approaches to the generalized problem of moments and their error analysis

de Klerk, E. & Laurent, M., Dec 2019, World Women in Mathematics 2018: Proceedings of the First World Meeting for Women in Mathematics (WM)². Araujo, C., Benkart, G., Praeger, C. E. & Tanbay, B. (eds.). Cham: Springer, p. 17-56 (Association for Women in Mathematics Series ; vol. 20).

Research output: Chapter in Book/Report/Conference proceedingChapterScientificpeer-review

Open Access
File
Convex Cone
Semidefinite Programming
Error Analysis
Moment
Outer Approximation
18 Downloads (Pure)

Polynomial norms

Ahmadi, A., de Klerk, E. & Hall, G., 2019, In : SIAM Journal on Optimization. 29, 1, p. 399–422

Research output: Contribution to journalArticleScientificpeer-review

Open Access
File
Polynomials
Norm
Polynomial
Positive definite
Sum of squares
2017

Solving Sparse Polynomial Optimization Problems with Chordal Structure Using the Sparse, Bounded-Degree Sum-of-Squares Hierarchy

Marandi, A., de Klerk, E. & Dahl, J., May 2017, Optimization Online.

Research output: Working paperDiscussion paperOther research output

Polynomials
46 Downloads (Pure)

Improved convergence rates for Lasserre-type hierarchies of upper bounds for box-constrained polynomial optimization

de Klerk, E., Hess, R. & Laurent, M., 2017, In : SIAM Journal on Optimization. 27, 1, p. 346-367

Research output: Contribution to journalArticleScientificpeer-review

Open Access
File
Sum of squares
Error Bounds
Convergence Rate
Polynomials
Upper bound

Convergence analysis for Lasserre's measure-based hierarchy of upper bounds for polynomial optimization

de Klerk, E., Laurent, M. & Sun, Z., Mar 2017, In : Mathematical Programming . 162, 1, p. 363-392

Research output: Contribution to journalArticleScientificpeer-review

Convergence Analysis
Compact Set
Probability density function
Polynomials
Upper bound

Bound-constrained polynomial optimization using only elementary calculations

de Klerk, E., Lasserre, J. B., Laurent, M. & Sun, Z., Aug 2017, In : Mathematics of Operations Research. 42, 3, p. 834-853

Research output: Contribution to journalArticleScientificpeer-review

Hypercube
Polynomials
Polynomial
Optimization
Rate of Convergence
2019
16 Downloads (Pure)

Distributionally robust optimization with polynomial densities: Theory, models and algorithms

de Klerk, E., Kuhn, D. & Postek, K. S., Sep 2019, In : Mathematical Programming .

Research output: Contribution to journalArticleScientificpeer-review

Robust Optimization
Model Theory
Polynomials
Polynomial
Sum of squares
2017
14 Downloads (Pure)

Comparison of Lasserre's Measure-based Bounds for Polynomial Optimization to Bounds Obtained by Simulated Annealing

de Klerk, E. & Laurent, M., Mar 2017, Ithaca: Cornell University Library, 12 p. (arXiv; vol. 1703.00744).

Research output: Working paperOther research output

Open Access
File
Simulated Annealing
Polynomial
Optimization
Convex Body
Compact Set
2016

[Review of the book An Introduction to Polynomial and Semi-Algebraic Optimization, Jean-Bernard Lasserre, 2015]

de Klerk, E., 2016, In : European Journal of Operational Research. 249, 2, p. 789-790 2 p.

Research output: Contribution to journalBook/Film/Article reviewOther research output

Polynomials
Polynomial
Optimization
Global optimization
Semidefinite Programming