Efficient implementation of an active set algorithm for large-scale portfolio selection

Solving the mean–variance customer portfolio in Markov chains using iterated quadratic/Lagrange programming: A credit-card customer limits approach

“…A portfolio is optimal if no other possible portfolio is able to improve the optimization criteria. Several methods has been studied in depth in optimization problem theory (Aouni, Colapinto, & La Torre, 2014;Athan & Papalambros, 1996;Bana e Costa & Soares, 2004;Ben Abdelaziz, Aouni, & El-Fayedh, 2007;Best & Hlouskova, 2000;Charnes, Clower, & Kortanek, 1967;Charnes & Cooper, 1977;Das & Dennis, 1998;Deng, Li, & Wang, 2005;Gram & Schyns, 2003;Hirschberger, Qi, & Steuer, 2010;Huang, 2007;Kolm, Ttnc, & Fabozzi, 2014;Korhonen & Yu, 1998;Messac, 1996;Owadally & Landsman, 2013;Qi, Hirschberger, & Steuer, 2009;Stein, Branke, & Schmeck, 2008;Steuer, Qi, & Hirschberger, 2011). Surveys can be found in Marler and Arora (2004), Metaxiotis and Liagkouras (2012) and Rifki and Ono (2012).…”

“…Therefore, well-spaced points can be shaped on the front to support the process of decision making. A few algorithms attempt to give a continuous representation of the Pareto-optimal front as the result of the optimization process to convex portfolio problems (Best & Hlouskova, 2000;Hirschberger et al, 2010;Korhonen & Yu, 1998;Niedermayer & Niedermayer, 2010;Stein et al, 2008;Steuer et al, 2011). The last four proposed continuous bi-objective and tri-objective problems using parametric quadratic programming.…”

On the criterion vectors of lines of portfolio selection with multiple quadratic and multiple linear objectives

“…Markowitz (1956) proposes a critical-line algorithm to compute nondominated sets. Then, Best (1996), Stein et al (2008), Niedermayer and Another justification of this paper is by the structure of efficient sets of portfolio selection models. For Markowitz's (1959) portfolio selection models, Markowitz (1956) proves that the efficient sets are piece-wisely made up by linear segments.…”

A model of portfolio optimization using time adapting genetic network programming

“…The meanvariance framework is so intuitive and strong that it has been widely applied to different areas within finance and risk management. In the case of linear constraints, Stein et al [4] solve the problem efficiently by parametric quadratic programming. However, there are many real-world nonlinear constraints which limit the number of different assets in a portfolio.…”