@article{Pinheiro2024,

title = {Mixed-integer quadratic optimization and iterative clustering techniques for semi-supervised support vector machines},

author = {Maria Eduarda Pinheiro, Jan Pablo Burgard and Martin Schmidt},

url = {https://link.springer.com/article/10.1007/s11750-024-00668-w},

year  = {2024},

date = {2024-05-16},

urldate = {2024-05-16},

journal = {Transactions in Operations Research (TOP)},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Schlegel2022,

title = {Shape Optimization for the Mitigation of Coastal Erosion via Porous Shallow Water Equations},

author = {L. Schlegel and V. Schulz},

doi = { https://doi.org/10.1002/nme.7074},

year  = {2022},

date = {2022-07-11},

journal = {International Journal for Numerical Methods in Engineering},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Burgard_et_al:2022b,

title = {Decomposition Methods for Robustified κ-Means Clustering Problems: If Less Conservative Does Not Mean Less Bad},

author = {Jan Pablo Burgard and Carina Moreira Costa and Martin Schmidt},

doi = {10.1007/s10479-022-04818-w},

year  = {2022},

date = {2022-01-01},

urldate = {2022-01-01},

journal = {Annals of Operations Research},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Costa_et_al:2022,

title = {An Alternating Method for Cardinality-Constrained Optimization: A Computational Study for the Best Subset Selection and Sparse Portfolio Problem},

author = {Carina Moreira Costa and Dennis Kreber and Martin Schmidt},

doi = {10.1287/ijoc.2022.1211},

year  = {2022},

date = {2022-01-01},

journal = {INFORMS Journal on Computing},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Costa_et_al:2022b,

title = {An Alternating Method for Cardinality-Constrained Optimization: A Computational Study for the Best Subset Selection and Sparse Portfolio Problem},

author = {Carina Moreira Costa and Dennis Kreber and Martin Schmidt},

doi = {10.1287/ijoc.2022.1211},

year  = {2022},

date = {2022-01-01},

urldate = {2022-01-01},

journal = {INFORMS Journal on Computing},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Beck_et_al:2022b,

title = {A robust approach for modeling limited observability in bilevel optimization},

author = {Yasmine Beck and Martin Schmidt},

doi = {10.1016/j.orl.2021.07.010},

issn = {0167-6377},

year  = {2022},

date = {2022-01-01},

volume = {49},

number = {5},

pages = {752--758},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{etna_vol56_pp209-234,

title = {A hybrid objective function for robustness of artificial neural networks-estimation of parameters in a mechanical system},

author = {J. Sokolowski and V. Schulz and H.P. Beise and U. Schroeder},

doi = {10.1553/etna_vol56s209},

year  = {2022},

date = {2022-01-01},

urldate = {2022-01-01},

journal = {Electron. Trans. Numer. Anal.},

volume = {56},

pages = {209-234},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Sembach2021,

title = {A Riemannian Newton trust-region method for fitting Gaussian mixture models},

author = {L. Sembach and J. P. Burgard and V. Schulz},

url = {https://link.springer.com/content/pdf/10.1007/s11222-021-10071-1.pdf},

doi = {https://doi.org/10.1007/s11222-021-10071-1},

year  = {2021},

date = {2021-12-17},

urldate = {2021-12-17},

journal = {Statistics and Computing},

volume = {32},

number = {8},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Schmitt2021,

title = {Tensor Method for Optimal Control Problems Constrained by Fractional 3D Elliptic Operator with Variable Coefficients},

author = {B. Schmitt and B. Khoromskij and V. Schulz},

year  = {2021},

date = {2021-07-19},

journal = {Numerical Linear Algebra with Applications},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Belak2021b,

title = {Branching Diffusions with Jumps and Valuation with Systemic Counterparties},

author = {C. Belak and D. Hoffmann and F. Seifried},

year  = {2021},

date = {2021-05-05},

journal = {Journal of Computational Finance},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Burgard2021,

title = {A Riemannian Newton Trust-Region Algorithm for Fitting Gaussian Mixture Models},

author = {J. P. Burgard and V. Schulz and L. Sembach},

url = {https://arxiv.org/abs/2104.14957},

year  = {2021},

date = {2021-05-05},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Siebenborn2021,

title = {A Multigrid Preconditioner for Tensor Product Spline Smoothing},

author = {M. Siebenborn and J. Wagner},

url = {https://arxiv.org/abs/1901.00654},

doi = {https://doi.org/10.1007/s00180-021-01104-4},

year  = {2021},

date = {2021-04-30},

journal = {Computational Statistics},

abstract = {Penalized spline smoothing is a well-established, nonparametric regression method that is efficient for one and two covariates. Its extension to more than two covariates is straightforward but suffers from exponentially increasing memory demands and computational complexity, which brings the method to its numerical limit. Penalized spline smoothing with multiple covariates requires solving a large-scale, regularized least-squares problem where the occurring matrices do not fit into storage of common computer systems. To overcome this restriction, we introduce a matrix-free implementation of the conjugate gradient method. We further present a matrix-free implementation of a simple diagonal as well as more advanced geometric multigrid preconditioner to significantly speed up convergence of the conjugate gradient method. All algorithms require a negligible amount of memory and therefore allow for penalized spline smoothing with multiple covariates. Moreover, for arbitrary but fixed covariate dimension, we show grid independent convergence of the multigrid preconditioner which is fundamental to achieve algorithmic scalability.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{https://doi.org/10.1002/zamm.202000287b,

title = {Efficient graph-based tensile strength simulations of random fiber structures},

author = {M. Harmening and N. Marheineke and R. Wegener},

url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/zamm.202000287},

doi = {https://doi.org/10.1002/zamm.202000287},

year  = {2021},

date = {2021-03-05},

journal = {ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift f\"{u}r Angewandte Mathematik und Mechanik},

abstract = {Abstract In this paper, we propose a model-simulation framework for virtual tensile strength testing of random fiber structures, such as those in nonwoven materials. The focus is on efficient handling of the problem-inherent multi-scales and randomness. In particular, the interplay between random microstructure and deterministic structural production-related features on the macro-scale makes classical homogenization-based approaches computationally complex and costly. In our approach we model the fiber structure as graph-based and of truss-type, equipped with a nonlinear elastic material law. The tensile strength test is described by a sequence of force equilibria with varied boundary conditions. Its embedding into a singularly perturbed dynamical system is advantageous with respect to statements on solution theory and convergence of numerical methods. A problem-tailored data reduction provides additional speed-up, while Monte-Carlo simulations account for randomness. This work serves as a proof of concept and opens the field for optimization.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Beck_et_al:2022b,

title = {A Robust Approach for Modeling Limited Observability in Bilevel Optimization},

author = {Y. Beck and M. Schmidt},

url = {http://www.optimization-online.org/DB_HTML/2021/01/8200.html},

year  = {2021},

date = {2021-01-08},

urldate = {2021-01-08},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Gabriel_et_al:2021bb,

title = {On linear bilevel optimization problems with complementarity-constrained lower levels},

author = {Steven A. Gabriel and Marina Leal and Martin Schmidt},

doi = {10.1080/01605682.2021.2015254},

year  = {2021},

date = {2021-01-01},

journal = {Journal of the Operational Research Society},

publisher = {Taylor \& Francis},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Gabriel_et_al:2021b,

title = {On linear bilevel optimization problems with complementarity-constrained lower levels},

author = {Steven A. Gabriel and Marina Leal and Martin Schmidt},

doi = {10.1080/01605682.2021.2015254},

year  = {2021},

date = {2021-01-01},

urldate = {2021-01-01},

journal = {Journal of the Operational Research Society},

publisher = {Taylor \& Francis},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Gabriel_et_al:2021,

title = {Solving Binary-Constrained Mixed Complementarity Problems Using Continuous Reformulations},

author = {S. A. Gabriel and M. Leal and M. Schmidt},

url = {https://www.sciencedirect.com/science/article/pii/S0305054820303257},

doi = {10.1016/j.cor.2020.105208},

year  = {2021},

date = {2021-01-01},

journal = {Computers \& Operations Research},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Belak2021bb,

title = {Continuous-Time Mean Field Games with Finite State Space and Common Noise},

author = {C. Belak and D. Hoffmann and F. Seifried },

year  = {2021},

date = {2021-01-01},

journal = {Applied Mathematics and Optimization (2021+)},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Frerick_et_al:2020bb,

title = {Complementarity Modeling of a Ramsey-Type Equilibrium Problem with Heterogeneous Agents},

author = {L. Frerick and G. M\"{u}ller-F\"{u}rstenberger and M. Schmidt and M. Sp\"{a}th},

year  = {2021},

date = {2021-01-01},

journal = {Computational Economics},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Roland2020,

title = {Mixed-integer nonlinear optimization for district heating network expansion},

author = { M. Roland and M. Schmidt },

url = {https://www.degruyter.com/view/journals/auto/68/12/article-p985.xml},

doi = {https://www.degruyter.com/view/journals/auto/68/12/article-p985.xml},

issn = {2196-677X},

year  = {2020},

date = {2020-12-01},

journal = {at - Automatisierungstechnik},

volume = {68},

number = {12},

pages = {985-1000},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{dVV-2020,

title = {Matroidal Approximations of Independence Systems},

author = {S. de Vries and R. V. Vohra},

url = {https://arxiv.org/abs/1906.06217},

year  = {2020},

date = {2020-07-14},

journal = {Operations Research Letters},

volume = {48},

pages = {587-593},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{DGV2020,

title = {A cookbook for finite element methods for nonlocal problems, including quadrature rule choices and the use of approximate balls.},

author = {M. D'Elia and M. Gunzburger and C. Vollmann},

url = {https://arxiv.org/abs/2005.10775},

year  = {2020},

date = {2020-05-21},

journal = {Mathematical Models and Methods in Applied Sciences (M3AS)},

volume = {31},

note = {accepted in M3AS},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{LEAL2020,

title = {Portfolio problems with two levels decision-makers: Optimal portfolio selection with pricing decisions on transaction costs},

author = {M. Leal and D. Ponce and J. Puerto},

url = {http://www.sciencedirect.com/science/article/pii/S0377221719310793},

doi = {https://doi.org/10.1016/j.ejor.2019.12.039},

issn = {0377-2217},

year  = {2020},

date = {2020-01-01},

journal = {European Journal of Operational Research},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{M\"{u}ller2020,

title = {Optimization of an Externally Mixed Biogas Plant Using a Robust CFD Method},

author = {J. M\"{u}ller and C. Schenk and R. Keicher and D. Schmidt and V. Schulz and K. Velten},

year  = {2020},

date = {2020-01-01},

journal = {Computers and Electronics in Agriculture},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{pp:stahl:2020,

title = {Efficient State Estimation for Gas Networks via Low-Rank Approximations},

author = {N. Stahl and N. Marheineke},

year  = {2020},

date = {2020-01-01},

journal = {IEEE Control System Letters},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{GROETZNER20201,

title = {A factorization method for completely positive matrices},

author = {P. Groetzner and M. D\"{u}r},

url = {http://www.sciencedirect.com/science/article/pii/S0024379519305385},

doi = {https://doi.org/10.1016/j.laa.2019.12.024},

issn = {0024-3795},

year  = {2020},

date = {2020-01-01},

journal = {Linear Algebra and its Applications},

volume = {591},

pages = {1 - 24},

abstract = {A matrix A is called completely positive, if there exists an entrywise nonnegative matrix B such that A=BBT. These matrices play a major role in combinatorial and quadratic optimization. In this paper, we study the problem of finding a nonnegative factorization BBT of a given completely positive matrix A. We formulate this factorization problem as a nonconvex feasibility problem and develop a solution method based on alternating projections. A local convergence result can be shown for this algorithm. We also provide a heuristic extension which improves the numerical performance of the algorithm. Extensive numerical tests show that the factorization method is very fast in most of the test instances and performs better than existing algorithms.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{deVries2020,

title = {A Smaller Extended Formulation for the Odd Cycle Inequalities of the Stable Set Polytope},

author = {S. de Vries and B. Perscheid },

url = {https://doi.org/10.1016/j.dam.2020.10.006},

year  = {2020},

date = {2020-01-01},

journal = {Discrete Applied Mathematics},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{devriesfriedrichperscheid,

title = {An Extended Formulation for the 1-Wheel Inequalities of the Stable Set Polytope},

author = {S. de Vries and U. Friedrich and B. Perscheid},

url = {https://doi.org/10.1002/net.21906},

doi = {10.1002/net.21906},

year  = {2020},

date = {2020-01-01},

journal = {Networks, 75:1},

pages = {86-94},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{VS2019,

title = {Exploiting Multilevel Toeplitz Structures in High Dimensional Nonlocal Diffusion},

author = {C. Vollmann and V. Schulz},

doi = {10.1007/s00791-018-00306-6},

issn = {1433-0369},

year  = {2019},

date = {2019-02-08},

journal = {Comput. Vis. Sci.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}