Bounds on efficient outcomes for large-scale cardinality-constrained Markowitz problems

Janusz Miroforidis ()
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Janusz Miroforidis: Polish Academy of Sciences

Journal of Global Optimization, 2021, vol. 80, issue 3, No 5, 617-634

Abstract: Abstract When solving large-scale cardinality-constrained Markowitz mean–variance portfolio investment problems, exact solvers may be unable to derive some efficient portfolios, even within a reasonable time limit. In such cases, information on the distance from the best feasible solution, found before the optimization process has stopped, to the true efficient solution is unavailable. In this article, I demonstrate how to provide such information to the decision maker. I aim to use the concept of lower bounds and upper bounds on objective function values of an efficient portfolio, developed in my earlier works. I illustrate the proposed approach on a large-scale data set based upon real data. I address cases where a top-class commercial mixed-integer quadratic programming solver fails to provide efficient portfolios attempted to be derived by Chebyshev scalarization of the bi-objective optimization problem within a given time limit. In this case, I propose to transform purely technical information provided by the solver into information which can be used in navigation over the efficient frontier of the cardinality-constrained Markowitz mean–variance portfolio investment problem.

Keywords: Bi-objective optimization; Multiple criteria decision making; Cardinality-constrained Markowitz portfolio investment problem; Two-sided efficient frontier approximations; Chebyshev scalarization (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10898-021-01022-1

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