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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Complexity bounds for primal-dual methods minimizing the model of objective function. Algorithm of price adjustment for market equilibrium. Portfolio choice based on third-degree stochastic dominance, with an application to industry momentum.
We develop and implement a portfolio optimization method for building investment portfolios that dominate a given benchmark index in terms of third-degree stochastic dominance. Our approach relies on the properties of the semi-variance function, a refinement of an existing 'super-convex' Programowanie kwadratowe we wspomaganiu decyzji. Measurement of interest rates using a convex optimization model. Arbitragetheorie und konvexe Steuern. Location choice and risk attitude of a decision maker.
A unified framework for the scheduling of guaranteed targeted display advertising under reach and frequency requirements.
The generalized independent set problem : polyhedral analysis and solution approaches. Resource allocation problems in decentralized energy management. Klauw, Thijs van der ; Gerards, Marco E. A note on heuristic approach based on UBQP formulation of the maximum diversity problem.
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.
Lecturer Prof. Frank Vallentin. Coordination of the Exercise Sessions Dr. Anna Gundert , Dr. Frederik von Heymann.