Veröffentlichungen

@article{07914d02d5a34ebba61601f8af258a2e,

title = "A Trust‐Region Method for p‐Harmonic Shape Optimization",

abstract = "The appropriate scaling of deformation fields has a significant impact on the performance of shape optimization algorithms. We introduce a pointwise gradient constraint to an efficient algorithm for -Laplace problems, while the complexity of the algorithm remains polynomial. Using this algorithm, we compute descent directions for shape optimization using -harmonic approach that fulfill a trust-region type constraint. Numerical experiments show the advantages of deformations computed with this approach when compared to deformations that are scaled after computation. This considers, in particular, the approximation of the limit setting and the preservation of mesh quality during an optimization with a fixed step size.",

author = "Henrik Wyschka and Winnifried Wollner",

year = "2025",

month = feb,

day = "5",

doi = "10.1002/pamm.70000",

language = "English",

volume = "25",

journal = "Proceedings in applied mathematics and mechanics",

issn = "1617-7061",

publisher = "Wiley-VCH Verlag",

number = "1",

@article{9c86c2706cce41e5a3c2d6f8d57dd758,

title = "Shape Optimization of Optical Microscale Inclusions",

abstract = "This paper describes a class of shape optimization problems for optical metamaterials comprised of periodic microscale inclusions composed of a dielectric, low-dimensional material suspended in a nonmagnetic bulk dielectric. The shape optimization approach is based on a homogenization theory for time-harmonic Maxwell{\textquoteright}s equations that describes effective material parameters for the propagation of electromagnetic waves through the metamaterial. The control parameter of the optimization is a deformation field representing the deviation of the microscale geometry from a reference configuration of the cell problem. This allows for describing the homogenized effective permittivity tensor as a function of the deformation field. We show that the underlying deformed cell problem is well-posed and regular. This, in turn, proves that the shape optimization problem is well-posed. In addition, a numerical scheme is formulated that utilizes an adjoint formulation with either gradient descent or BFGS as optimization algorithms. The developed algorithm is tested numerically on a number of prototypical shape optimization problems with a prescribed effective permittivity tensor as the target.",

author = "Manaswinee Bezbaruah and Matthias Maier and Winnifried Wollner",

year = "2024",

month = aug,

day = "31",

doi = "10.1137/23M158262X",

language = "English",

volume = "46",

pages = "B377 -- B402",

journal = "SIAM Journal on Scientific Computing",

issn = "1064-8275",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "4",

@article{b1581db9e2ef40a096f8dab5a5bda377,

title = "A Successive Linear Relaxation Method for MINLPs with Multivariate Lipschitz Continuous Nonlinearities",

abstract = "We present a novel method for mixed-integer optimization problems with multivariate and Lipschitz continuous nonlinearities. In particular, we do not assume that the nonlinear constraints are explicitly given but that we can only evaluate them and that we know their global Lipschitz constants. The algorithm is a successive linear relaxation method in which we alternate between solving a master problem, which is a mixed-integer linear relaxation of the original problem, and a subproblem, which is designed to tighten the linear relaxation of the next master problem by using the Lipschitz information about the respective functions. By doing so, we follow the ideas of Schmidt, Sirvent, and Wollner (Math Program 178(1):449–483 (2019) and Optim Lett 16(5):1355-1372 (2022)) and improve the tackling of multivariate constraints. Although multivariate nonlinearities obviously increase modeling capabilities, their incorporation also significantly increases the computational burden of the proposed algorithm. We prove the correctness of our method and also derive a worst-case iteration bound. Finally, we show the generality of the addressed problem class and the proposed method by illustrating that both bilevel optimization problems with nonconvex and quadratic lower levels as well as nonlinear and mixed-integer models of gas transport can be tackled by our method. We provide the necessary theory for both applications and briefly illustrate the outcomes of the new method when applied to these two problems.",

keywords = "Bilevel optimization, Gas networks, Global optimization, Lipschitz optimization, Mixed-integer nonlinear optimization",

author = "Julia Gr{\"u}bel and Richard Krug and Martin Schmidt and Winnifried Wollner",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s).",

year = "2023",

month = sep,

doi = "10.1007/s10957-023-02254-9",

language = "English",

volume = "198",

pages = "1077--1117",

journal = "Journal of Optimization Theory and Applications",

issn = "0022-3239",

publisher = "Springer New York",

number = "3",

@article{e18a3bc44ada4c709d555b9eb6f22f65,

title = "Gradient Robust Mixed Methods for Nearly Incompressible Elasticity",

abstract = "Within the last years pressure robust methods for the discretization of incompressible fluids have been developed. These methods allow the use of standard finite elements for the solution of the problem while simultaneously removing a spurious pressure influence in the approximation error of the velocity of the fluid, or the displacement of an incompressible solid. To this end, reconstruction operators are utilized mapping discretely divergence free functions to divergence free functions. This work shows that the modifications proposed for Stokes equation by Linke (Comput Methods Appl Mech Eng 268:782–800, 2014) also yield gradient robust methods for nearly incompressible elastic materials without the need to resort to discontinuous finite elements methods as proposed in Fu et al. (J Sci Comput 86(3):39–30, 2021).",

author = "Basava, {Seshadri R.} and Winnifried Wollner",

year = "2023",

month = jun,

doi = "10.1007/s10915-023-02227-0",

language = "English",

volume = "95",

journal = "Journal of Scientific Computing",

issn = "0885-7474",

publisher = "Springer New York",