On convex multiobjective programs with application to portfolio optimization

Jayasekara, Pubudu L.W.; Adelgren, Nathan; Wiecek, Margaret M.

doi:10.1002/mcda.1690

Cited by 15 publications

(6 citation statements)

References 47 publications

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“…Comprehensive overviews of the state of the art in the field of portfolio optimization can be found, for example, in Jayasekara et al (2019), Mansini et al (2014), and Zhang et al (2018).…”

Section: A General Overviewmentioning

confidence: 99%

Expected mean return—standard deviation efficient frontier approximation with low‐cardinality portfolios in the presence of the risk‐free asset

Juszczuk

Kaliszewski

Miroforidis

et al. 2022

Int Trans Operational Res

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In the expected mean return, standard deviation portfolio selection problem, the first step is usually to derive the set of efficient portfolios, which in the space of objective function values is represented by the efficient frontier. With modern methods and software, it is an easy task even for thousands of assets provided that the problem is continuous. However, investors often introduce the requirement to limit the number of assets in portfolios (portfolio cardinality). The resulting mixed-integer quadratic formulations are computationally much more complex. In this work, we assume that besides risky assets, the risk-free asset is available to the investor, and short selling is not allowed. Since in this case the efficient frontier cannot be directly derived by a quadratic solver, we propose a naive but intuitive heuristic to approximate the efficient frontier in the presence of the risk-free asset. In contrast to the general-purpose evolutionary heuristics, we exploit the underlying mechanism of portfolio composition. We show by numerical experiments that in large-scale instances it works well, even compared to a state-of-the-art evolutionary multiobjective optimization algorithm. Moreover, the heuristic produces portfolios of remarkably limited cardinalities.

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“…Comprehensive overviews of the state of the art in the field of portfolio optimization can be found, for example, in Jayasekara et al (2019), Mansini et al (2014), and Zhang et al (2018).…”

Section: A General Overviewmentioning

confidence: 99%

Expected mean return—standard deviation efficient frontier approximation with low‐cardinality portfolios in the presence of the risk‐free asset

Juszczuk

Kaliszewski

Miroforidis

et al. 2022

Int Trans Operational Res

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show abstract

“…In the future, we will impose practical constraints in the form of inequality to (4) – (5) , but we will lose the analytical solutions. Hirschberger et al, Jayasekara et al [78] , [79] propose parametric-quadratic programming to solve a general multiple-objective portfolio-selection model (3) . We will try to exploit the numerical solutions (rather than the analytical solutions).…”

Section: Performing Robust Optimization For (5)mentioning

confidence: 99%

Originating multiple-objective portfolio selection by counter-COVID measures and analytically instigating robust optimization by mean-parameterized nondominated paths

Liao

Liu

et al. 2022

Operations Research Perspectives

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“…BOMINLP (1) may have an innite number of non-dominated points due to the continuous variables. To our knowledge, the only method to compute an explicit description of the non-dominated set of continuous MOPs is a very recent one presented in Jayasekara et al (2019). In their approach, which they demonstrate on problems with a small number of variables, the authors are able to solve convex MOP problems where all the objectives are quadratic ones.…”

Section: Introductionmentioning

confidence: 99%

Bi-objective optimisation over a set of convex sub-problems

et al. 2021

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During the last decades, research in multi-objective optimisation (MO) has seen considerable growth. However, this activity has been focused on linear, non-linear, and combinatorial optimisation with multiple objectives. Multiobjective mixed integer (linear or non-linear) programming has received considerably less attention. In this paper we propose an algorithm to compute a nite set of non-dominated points/ecient solutions of a bi-objective mixed binary optimisation problems for which the sub-problems obtained when xing the binary variables are convex, and there is a nite set of feasible binary variable vectors.Our method uses bound sets and exploits the convexity property of the subproblems to nd a set of ecient solutions for the main problem. Our algorithm creates and iteratively updates bounds for each vector in the set of feasible binary variable vectors, and uses these bounds to guarantee that a set of exact non-dominated points is generated. For instances where the set of feasible binary variable vectors is too large to generate such provably optimal solutions within a reasonable time, our approach can be used as a matheuristic by heuristically selecting a promising subset of binary variable vectors to explore. This investigation is motivated by the problem of beam angle optimisation arising in radiation therapy planning, which we solve heuristically to provide numerical results.

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On convex multiobjective programs with application to portfolio optimization

Cited by 15 publications

References 47 publications

Expected mean return—standard deviation efficient frontier approximation with low‐cardinality portfolios in the presence of the risk‐free asset

Expected mean return—standard deviation efficient frontier approximation with low‐cardinality portfolios in the presence of the risk‐free asset

Originating multiple-objective portfolio selection by counter-COVID measures and analytically instigating robust optimization by mean-parameterized nondominated paths

Bi-objective optimisation over a set of convex sub-problems

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