AutorIn Dipl. To this end, we are also making use of monotone operator theory as some of the provided algorithms are originally designed to solve monotone inclusion problems. After introducing basic notations and preliminary results in convex analysis, we derive two numerical methods based on different smoothing strategies for solving nondifferentiable convex optimization problems. The first approach, known as the double smoothing technique, solves the optimization problem with some given a priori accuracy by applying two regularizations to its conjugate dual problem. A special fast gradient method then solves the regularized dual problem such that an approximate primal solution can be reconstructed from it. The second approach affects the primal optimization problem directly by applying a single regularization to it and is capable of using variable smoothing parameters which lead to a more accurate approximation of the original problem as the iteration counter increases.

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Publications Events. Your search terms. Open Access only. Narrow search. Narrow search Year of publication. Online availability. Type of publication. Type of publication narrower categories. Published in Showing 1 - 50 of Sort Relevance Date newest first Date oldest first. Multiple phase tabu search for bipartite boolean quadratic programming with partitioned variables.

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The boolean quadratic programming problem with generalized upper bound constraints. Wang, Yang ; Punnen, Abraham P. Robust revenue opportunity modeling with quadratic programming. Global optimization of a semiconductor IC supply chain network. Kalir, Adar A. Endogeneity of return parameters and portfolio selection : an analysis on implied covariances. Higher-degree stochastic dominance optimality and efficiency. Network pricing of congestion-free networks : the elastic and linear demand case.

Inexact proximal Newton methods for slef-concordant functions. Li, Jinchao ; Andersen, Martin S. Mean-variance optimal trading problem subject to stochastic dominance constraints with second order autoregressive price dynamics. Portfolio choice based on third-degree stochastic dominance.

A hybrid heuristic technique for optimal coordination in intermodal logistics scheduling. Local cuts and two-period convex hull closures for big-bucket lot-sizing problems. RAROC in portfolio optimization. Xidonas, Panagiotis ; Kountzakis, Christos E.

Stochastic modeling of natural gas infrastructure development in Europe under demand uncertainty. Research on the portfolio optimization model under quantitative constraint based on genetic algorithm. On linearization techniques for budget-constrained binary quadratic programming problems.

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Symbolik & Numerik – Mathematica 12: Convex Optimization

German original. In addition, knowledge of functional analysis is an advantage. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:.


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Version 12 expands the scope of optimization solvers in the Wolfram Language to include optimization of convex functions over convex constraints. Convex optimization is a class of problems for which there are fast and robust optimization algorithms, both in theory and in practice. Just as advances in linear optimization opened up many industrial applications, ever-wider classes of problems are being identified to be convex in a wide variety of domains, such as statistics, finance, signal processing, geometry and many more. Convex Optimization.


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Lecturer Prof. Frank Vallentin. Coordination of the Exercise Sessions Dr. Anna Gundert , Dr. Frederik von Heymann.

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