Martin Schmidt
YOU?
Author Swipe
View article: Publisher Correction: On a tractable single-level reformulation of a multilevel model of the European entry-exit gas market with market power
Publisher Correction: On a tractable single-level reformulation of a multilevel model of the European entry-exit gas market with market power Open
We propose a framework that allows to quantitatively analyze the interplay of the different agents involved in gas trade and transport in the context of the European entry-exit system. Previous contributions have focused on the case of per…
View article: Branch-and-Cut for Mixed-Integer Generalized Nash Equilibrium Problems
Branch-and-Cut for Mixed-Integer Generalized Nash Equilibrium Problems Open
Generalized Nash equilibrium problems with mixed-integer variables form an important class of games in which each player solves a mixed-integer optimization problem with respect to her own variables and the strategy space of each player de…
View article: Mixed-integer linear optimization for cardinality-constrained random forests
Mixed-integer linear optimization for cardinality-constrained random forests Open
Random forests are among the most famous algorithms for solving classification problems, in particular for large-scale data sets. Considering a set of labeled points and several decision trees, the method takes the majority vote to classif…
View article: Dinitrogen Activation with Low‐Valent Strontium
Dinitrogen Activation with Low‐Valent Strontium Open
DFT calculations on β‐diketiminate (BDI) complexes with the full series of alkaline‐earth (Ae) metals show that (BDI)AeAe(BDI) complexes of the heavier Ae metals (Ca, Sr, Ba) have long weak Ae─Ae bonds that are prone to homolytic bond clea…
View article: Adjustable robust nonlinear network design without controllable elements under load scenario uncertainties
Adjustable robust nonlinear network design without controllable elements under load scenario uncertainties Open
We study network design problems for nonlinear and nonconvex flow models without controllable elements under load scenario uncertainties, i.e., under uncertain injections and withdrawals. To this end, we apply the concept of adjustable rob…
View article: Heuristic Methods for Γ-Robust Mixed-Integer Linear Bilevel Problems
Heuristic Methods for Γ-Robust Mixed-Integer Linear Bilevel Problems Open
Because of their nested structure, bilevel problems are intrinsically hard to solve—even if all variables are continuous and all parameters of the problem are exactly known. In this paper, we study mixed-integer linear bilevel problems wit…
View article: On Coupling Constraints in Pessimistic Linear Bilevel Optimization
On Coupling Constraints in Pessimistic Linear Bilevel Optimization Open
The literature on pessimistic bilevel optimization with coupling constraints is rather scarce and it has been common sense that these problems are harder to tackle than pessimistic bilevel problems without coupling constraints. In this not…
View article: Solving Decision-Dependent Robust Problems as Bilevel Optimization Problems
Solving Decision-Dependent Robust Problems as Bilevel Optimization Problems Open
Both bilevel and robust optimization are established fields of mathematical optimization and operations research. However, only until recently, the similarities in their mathematical structure has neither been studied theoretically nor exp…
View article: Low-coordinate calcium peroxide and oxide complexes
Low-coordinate calcium peroxide and oxide complexes Open
A Ca I synthon is key to access low-coordinate Ca (per)oxide complexes of which especially the oxide complex is highly reactive and unstable.
View article: Reductive cyclotrimerization of CO and isonitriles with a highly reactive Ca <sup>I</sup> synthon
Reductive cyclotrimerization of CO and isonitriles with a highly reactive Ca <sup>I</sup> synthon Open
A strongly reducing Ca I synthon releases N 2 and two electrons for the reductive C–C coupling of CO and RNC.
View article: On coupling constraints in linear bilevel optimization
On coupling constraints in linear bilevel optimization Open
It is well-known that coupling constraints in linear bilevel optimization can lead to disconnected feasible sets, which is not possible without coupling constraints. However, there is no difference between linear bilevel problems with and …
View article: Adjustable Robust Nonlinear Network Design Without Controllable Elements under Load Scenario Uncertainties
Adjustable Robust Nonlinear Network Design Without Controllable Elements under Load Scenario Uncertainties Open
We study network design problems for nonlinear and nonconvex flow models without controllable elements under load scenario uncertainties, i.e., under uncertain injections and withdrawals. To this end, we apply the concept of adjustable rob…
View article: A tutorial on solving single‐leader‐multi‐follower problems using SOS1 reformulations
A tutorial on solving single‐leader‐multi‐follower problems using SOS1 reformulations Open
In this tutorial, we consider single‐leader‐multi‐follower games in which the models of the lower‐level players have polyhedral feasible sets and convex objective functions. This situation allows for classic Karush–Kuhn–Tucker reformulatio…
View article: Mixed-integer quadratic optimization and iterative clustering techniques for semi-supervised support vector machines
Mixed-integer quadratic optimization and iterative clustering techniques for semi-supervised support vector machines Open
Among the most famous algorithms for solving classification problems are support vector machines (SVMs), which find a separating hyperplane for a set of labeled data points. In some applications, however, labels are only available for a su…
View article: Mixed-Integer Linear Optimization for Cardinality-Constrained Random Forests
Mixed-Integer Linear Optimization for Cardinality-Constrained Random Forests Open
Random forests are among the most famous algorithms for solving classification problems, in particular for large-scale data sets. Considering a set of labeled points and several decision trees, the method takes the majority vote to classif…
View article: On the relation between affinely adjustable robust linear complementarity and mixed-integer linear feasibility problems
On the relation between affinely adjustable robust linear complementarity and mixed-integer linear feasibility problems Open
We consider adjustable robust linear complementarity problems and extend the results of Biefel et al. (SIAM J Optim 32:152–172, 2022) towards convex and compact uncertainty sets. Moreover, for the case of polyhedral uncertainty sets, we pr…
View article: On Coupling Constraints in Linear Bilevel Optimization
On Coupling Constraints in Linear Bilevel Optimization Open
It is well-known that coupling constraints in linear bilevel optimization can lead to disconnected feasible sets, which is not possible without coupling constraints. However, there is no difference between linear bilevel problems with and …
View article: Exact and Heuristic Solution Techniques for Mixed-Integer Quantile Minimization Problems
Exact and Heuristic Solution Techniques for Mixed-Integer Quantile Minimization Problems Open
We consider mixed-integer linear quantile minimization problems that yield large-scale problems that are very hard to solve for real-world instances. We motivate the study of this problem class by two important real-world problems: a maint…
View article: Relax and penalize: a new bilevel approach to mixed-binary hyperparameter optimization
Relax and penalize: a new bilevel approach to mixed-binary hyperparameter optimization Open
In recent years, bilevel approaches have become very popular to efficiently estimate high-dimensional hyperparameters of machine learning models. However, to date, binary parameters are handled by continuous relaxation and rounding strateg…
View article: Relax and penalize: a new bilevel approach to mixed-binary hyperparameter optimization
Relax and penalize: a new bilevel approach to mixed-binary hyperparameter optimization Open
In recent years, bilevel approaches have become very popular to efficiently estimate high-dimensional hyperparameters of machine learning models. However, to date, binary parameters are handled by continuous relaxation and rounding strateg…
View article: A Successive Linear Relaxation Method for MINLPs with Multivariate Lipschitz Continuous Nonlinearities
A Successive Linear Relaxation Method for MINLPs with Multivariate Lipschitz Continuous Nonlinearities Open
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 …
View article: Exact methods for discrete $${\varGamma }$$-robust interdiction problems with an application to the bilevel knapsack problem
Exact methods for discrete $${\varGamma }$$-robust interdiction problems with an application to the bilevel knapsack problem Open
Developing solution methods for discrete bilevel problems is known to be a challenging task—even if all parameters of the problem are exactly known. Many real-world applications of bilevel optimization, however, involve data uncertainty. W…
View article: Adaptive nonlinear optimization of district heating networks based on model and discretization catalogs
Adaptive nonlinear optimization of district heating networks based on model and discretization catalogs Open
We propose an adaptive optimization algorithm for operating district heating networks in a stationary regime. The behavior of hot water flow in the pipe network is modeled using the incompressible Euler equations and a suitably chosen ener…
View article: On a Computationally Ill-Behaved Bilevel Problem with a Continuous and Nonconvex Lower Level
On a Computationally Ill-Behaved Bilevel Problem with a Continuous and Nonconvex Lower Level Open
It is well known that bilevel optimization problems are hard to solve both in theory and practice. In this paper, we highlight a further computational difficulty when it comes to solving bilevel problems with continuous but nonconvex lower…
View article: Time-Domain Decomposition for Mixed-Integer Optimal Control Problems
Time-Domain Decomposition for Mixed-Integer Optimal Control Problems Open
We consider mixed-integer optimal control problems, whose optimality conditions involve global combinatorial optimization aspects for the corresponding Hamiltonian pointwise in time. We propose a time-domain decomposition, which makes this…
View article: Why there is no need to use a big-M in linear bilevel optimization: a computational study of two ready-to-use approaches
Why there is no need to use a big-M in linear bilevel optimization: a computational study of two ready-to-use approaches Open
Linear bilevel optimization problems have gained increasing attention both in theory as well as in practical applications of Operations Research (OR) during the last years and decades. The latter is mainly due to the ability of this class …