Modules

19 results

A1.4 Mathematics19

Discrete OptimizationNo ratings for this module yet.A1.4.2 Modules in OptimizationYou will learn central concepts and algorithms of linear integer optimization and combinatorial optimization. In the module you will analyze mathematical structures that allow efficient solution methods, and you will be able to model real problems as discrete optimization problems and identify special cases that are efficiently solvable.9 ECTSruns this semesterCIT413041Nichtlineare OptimierungNo ratings for this module yet.A1.4.2 Modules in OptimizationYou engage with theory and numerical methods of nonlinear optimization. You will learn advanced methods for unconstrained and, in particular, constrained optimization problems (e.g., SQP, barrier and interior-point methods) and you will be able to assess and apply convergence properties of such methods in the end.5 ECTSruns this semesterMA3503Algorithmic Game TheoryNo ratings for this module yet.A1.4.2 Modules in OptimizationYou will learn the fundamentals of algorithmic game theory at the intersection of computer science, mathematics, and economics. In this module you will deal with algorithmic aspects of game-theoretic solution concepts such as Nash equilibria and with the design of economic mechanisms; in the end you will be able to analyze these concepts algorithmically and in terms of complexity theory.5 ECTSno date this semesterIN2239Approximation AlgorithmsNo ratings for this module yet.A1.4.2 Modules in OptimizationYou learn how to design and analyze efficient approximation algorithms for combinatorial optimization problems. In the end you can assess the running time and approximation guarantees of algorithms, apply known techniques (e.g. Greedy, LP-Rounding, Primal-Dual), and prove limits of approximability.9 ECTSno date this semesterCIT4100003Case Studies OptimizationNo ratings for this module yet.A1.4.2 Modules in OptimizationYou work in small teams on concrete optimization tasks from discrete and non-linear optimization. You model real problems, select and implement suitable solution procedures with modern optimization tools, and present and assess the results both for a disciplinary audience and for a non-scientific audience.10 ECTSno date this semesterCIT413042
14 more in A1.4 MathematicsComputational Convexity - Optimal ContainmentNo ratings for this module yet.A1.4.2 Modules in OptimizationYou deal with algorithmic questions on convex problems in arbitrary dimensions and, to some extent, in generalized normed spaces. In the module you will learn typical problems such as optimal containment, the underlying concepts of convex analysis and techniques from linear optimization, as well as their algorithmic solution and analysis.9 ECTSno date this semesterMA5206Computational Integer ProgrammingNo ratings for this module yet.A1.4.2 Modules in OptimizationIn this module you learn the computational methods for solving mixed-integer optimization problems (MIP). You understand fundamental algorithms such as Simplex, Branch-and-Bound and Cutting-Plane-Separation as well as practical improvements and heuristics that make MIP solvers applicable to real problems. By the end you can explain these procedures, justify their correctness, and use your modeling knowledge to improve MIP models.3 ECTSno date this semesterMA8034Convex Duality and Applications in Mass Transport and Calculus of VariationsNo ratings for this module yet.A1.4.2 Modules in OptimizationYou will learn foundations of convex duality and how they are applied in variational problems and in the theory of optimal mass transport. In the end you will be able to understand Legendre/Fenchel duality, dual formulations of optimization problems and central results of mass transport theory as well as explain simple numerical procedures for it.3 ECTSno date this semesterMA5910First Order Primal-Dual Optimization MethodsNo ratings for this module yet.A1.4.2 Modules in OptimizationIn this module you will learn modern First-Order Primal-Dual optimization methods. You will understand how simple iterative schemes with primal-dual decompositions can be combined to design efficient, structure-exploiting algorithms for large-scale problems, and you will be able to apply and further investigate these methods.5 ECTSno date this semesterCIT413065Fundamentals of Optimization for Machine LearningNo ratings for this module yet.A1.4.2 Modules in OptimizationYou will learn fundamentals and advanced techniques of optimization, both convex and nonconvex as well as combinatorial and continuous, with a focus on applications in machine learning. In the end you will be able to understand optimization problems from ML research and approach research questions in this area.5 ECTSno date this semesterCIT413031Graph TheoryNo ratings for this module yet.A1.4.2 Modules in OptimizationYou learn the fundamentals of graph theory: paths and cycles, connectivity, trees, matchings, k-connectivity and Menger's theorem, as well as planar graphs and colorings. In the end you can apply central definitions and theorems, carry out proofs, and transfer the concepts presented to concrete problems and simple applications (including from data analysis).6 ECTSno date this semesterCIT413051Introduction to Regularization and Learning Methods for Inverse ProblemsNo ratings for this module yet.A1.4.2 Modules in OptimizationYou will learn the mathematical foundations of inverse problems and regularization as well as modern data-driven solution approaches. In the end you will be able to analyze inverse problems, apply classical regularization methods and classify data-based reconstruction methods.5 ECTSno date this semesterCIT413070Konvexe Optimierung für Computer VisionNo ratings for this module yet.A1.4.2 Modules in OptimizationYou will learn the fundamentals of convex analysis and their application to optimization problems in image processing and computer vision. After the module you will be able to understand, apply and implement common first-order and proximal methods for typical CV tasks (e.g., image reconstruction, segmentation, matrix factorization).6 ECTSno date this semesterIN2330Modern Methods in Nonlinear OptimizationNo ratings for this module yet.A1.4.2 Modules in OptimizationYou will learn selected modern methods of nonlinear optimization, e.g. convex and non-smooth optimization, interior-point methods, semidefinite programming, robustness concepts and duality. In the end you will be able to understand current research articles on the treated topics and you will be prepared to pursue your own research questions in nonlinear optimization.5 ECTSno date this semesterMA4503Nonsmooth OptimizationNo ratings for this module yet.A1.4.2 Modules in OptimizationYou will learn methods and concepts of nonsmooth optimization and how to apply them. The module conveys fundamentals of nonsmooth analysis, numerical procedures for minimization and for handling nonsmooth equations, as well as their convergence properties. At the end you will be able to select appropriate methods for concrete nonsmooth models and to assess their behavior theoretically.5 ECTSno date this semesterCIT4130020Optimal Transport, Numerics and SamplingNo ratings for this module yet.A1.4.2 Modules in OptimizationIn this module you will learn the theory of optimal transport and methods for its numerical treatment. You will understand the fundamental models (Monge, Kantorovich), important properties of Wasserstein spaces and gain an overview of numerical procedures and applications in Data Science.3 ECTSno date this semesterMA5933Optimale Steuerung gewöhnlicher Differentialgleichungen 1No ratings for this module yet.A1.4.2 Modules in OptimizationYou learn fundamental concepts and methods of optimal control for ordinary differential equations. In the end you will be able to formulate necessary optimality conditions (e.g., Euler–Lagrange, Legendre–Clebsch), distinguish different types of constraints and control restrictions, and convert control problems into boundary-value forms suitable for numerical treatment.5 ECTSno date this semesterMA3312Polyhedral CombinatoricsNo ratings for this module yet.A1.4.2 Modules in OptimizationYou learn how to approach combinatorial optimization problems through the geometry of polyhedra: representation of polytopes, the connection between geometry and optimization of linear functions, as well as modern algorithms such as branch-and-cut and separation/optimization. In the end you will be able to apply the methods to typical problems (e.g., matching, TSP polytopes) and assess their limits in the context of NP-hardness.6 ECTSno date this semesterMA5225Scheduling: Theory and AlgorithmsNo ratings for this module yet.A1.4.2 Modules in OptimizationYou will learn models and algorithms for the assignment of tasks to scarce resources. The module covers classical and modern scheduling problems (including stochastic, online, robust) as well as methods for their modeling, analysis and solution, so that you can, in the end, assess complexity, design exact or approximate algorithms and prove their quality.5 ECTSno date this semesterCIT413053