An Improved Frank–Wolfe Algorithm to Solve the Tactical Investment Portfolio Optimization Problem

Deva Putra Setyawan, Diah Chaerani () and Sukono Sukono
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Deva Putra Setyawan: Master of Mathematics Study Program, Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Bandung 45363, Indonesia
Diah Chaerani: Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Bandung 45363, Indonesia
Sukono Sukono: Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Bandung 45363, Indonesia

Mathematics, 2025, vol. 13, issue 18, 1-26

Abstract: Quadratic programming (QP) formulations are widely used in optimal investment portfolio selection, a central problem in financial decision-making. In practice, asset allocation decisions operate at two interconnected levels: the strategic level, which allocates the budget across major asset classes, and the tactical level, which distributes the allocation within each class to individual securities or instruments. This study evaluates the Frank–Wolfe (FW) algorithm as a computationally alternative to a QP formulation implemented in CVXPY and solved using OSQP (CVXPY–OSQP solver) for tactical investment portfolio optimization. By iteratively solving a linear approximation of the convex objective function, FW offers a distinct approach to portfolio construction. A comparative analysis was conducted using a tactical portfolio model with a small number of stock assets, assessing solution similarity, computational running time, and memory usage. The results demonstrate a clear trade-off between the two methods. While FW can produce portfolio weights closely matching those of the CVXPY–OSQP solver at lower and feasible target returns, its solutions differ at higher returns near the limits of the feasible set. However, FW consistently achieved shorter execution times and lower memory consumption. This study quantifies the trade-offs between accuracy and efficiency and identifies opportunities to improve FW’s accuracy through adaptive iteration strategies under more challenging optimization conditions.

Keywords: Frank-Wolfe algorithm; quadratic programming; tactical investment portfolio optimization; computational efficiency; portfolio management (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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