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

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 best feasible solution, found before optimization process has stopped, true solution is unavailable. this article, I demonstrate how provide decision maker. aim use concept of lower bounds and upper objective function values an portfolio, developed in my earlier works. illustrate proposed approach data set based upon real data. address cases where top-class commercial mixed-integer quadratic programming solver fails portfolios attempted derived by Chebyshev scalarization bi-objective problem given case, propose transform purely technical provided into which can used navigation over frontier problem.