Practical algorithms for value-at-risk portfolio optimization problems

Feng, Mingbin; Wächter, Andreas; Staum, Jeremy

doi:10.1080/21649502.2014.995214

Cited by 18 publications

(12 citation statements)

References 14 publications

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“…66 However, it is argued that Big-M formulations remain the most practical way for solving DI problems (which they refer to as VaR problems). 67 A common alternative approach is to use the meta-heuristic simulated annealing to find good results within a short time. This has been studied in Refs.…”

Section: B3 Properties and Solutions Methodsmentioning

confidence: 99%

“…The computational difficulties of this model are not surprising because models with indicator variables and constraints are known to have weak linear programming relaxations and to be hard to solve 66 . However, it is argued that Big‐M formulations remain the most practical way for solving DI problems (which they refer to as VaR problems) 67 . A common alternative approach is to use the meta‐heuristic simulated annealing to find good results within a short time.…”

Section: Mathematical Modelsmentioning

confidence: 99%

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Optimization in treatment planning of high dose‐rate brachytherapy — Review and analysis of mathematical models

2021

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Treatment planning in high dose-rate brachytherapy has traditionally been conducted with manual forward planning, but inverse planning is today increasingly used in clinical practice. There is a large variety of proposed optimization models and algorithms to model and solve the treatment planning problem. Two major parts of inverse treatment planning for which mathematical optimization can be used are the decisions about catheter placement and dwell time distributions. Both these problems as well as integrated approaches are included in this review. The proposed models include linear penalty models, dose-volume models, mean-tail dose models, quadratic penalty models, radiobiological models, and multiobjective models. The aim of this survey is twofold: (i) to give a broad overview over mathematical optimization models used for treatment planning of brachytherapy and (ii) to provide mathematical analyses and comparisons between models. New technologies for brachytherapy treatments and methods for treatment planning are also discussed. Of particular interest for future research is a thorough comparison between optimization models and algorithms on the same dataset, and clinical validation of proposed optimization approaches with respect to patient outcome.

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Section: B3 Properties and Solutions Methodsmentioning

confidence: 99%

Section: Mathematical Modelsmentioning

confidence: 99%

Optimization in treatment planning of high dose‐rate brachytherapy — Review and analysis of mathematical models

2021

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“…The computational difficulties of this model are not surprising because models with indicator constraints are known to have weak linear programming relaxations and to be hard to solve [13]. However, in [36] it is argued that Big M formulations remains the most practical way for solving DI problems (they use the term VaR problems). A common alternative approach is to use the heuristic simulated annealing to find good results within a short time.…”

Section: Properties and Solutions Methodsmentioning

confidence: 99%

Mathematical Modelling of Dose Planning in High Dose-Rate Brachytherapy

Morén

2019

Linköping Studies in Science and Technology. Licentiate Thesis

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“…where M is an arbitrary large positive constant. Feng et al [12] proposed algorithms to assign an appropriate value to M in the above optimization problem.…”

Section: 2mentioning

confidence: 99%

Worst-case analysis of Gini mean difference safety measure

Sehgal¹,

Mehra²

2021

JIMO

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The paper introduces the worst-case portfolio optimization models within the robust optimization framework for maximizing return through either the mean or median metrics. The risk in the portfolio is quantified by Gini mean difference. We put forward the worst-case models under the mixed and interval+polyhedral uncertainty sets. The proposed models turn out to be linear and mixed integer linear programs under the mixed uncertainty set, and semidefinite program under interval+polyhedral uncertainty set. The performance comparison of the proposed models on the listed stocks of Euro Stoxx 50, Dow Jones Global Titans 50, S&P Asia 50, consistently exhibit advantage over their conventional non-robust counterpart models on various risk parameters including the standard deviation, worst return, value at risk, conditional value at risk and maximum drawdown of the portfolio.2010 Mathematics Subject Classification. Primary: 91G10, 91B30, 62G35; Secondary: 90C90, 90C05, 90C11.

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Practical algorithms for value-at-risk portfolio optimization problems

Cited by 18 publications

References 14 publications

Optimization in treatment planning of high dose‐rate brachytherapy — Review and analysis of mathematical models

Optimization in treatment planning of high dose‐rate brachytherapy — Review and analysis of mathematical models

Mathematical Modelling of Dose Planning in High Dose-Rate Brachytherapy

Worst-case analysis of Gini mean difference safety measure

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