2017/05/16 by Alper Atamtürk, Atamturk, Alper, Hyemin Jeon +1
Decision Sciences · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Multi-Criteria Decision Making #Optimization and Control (math.OC) #Risk and Portfolio Optimization
paper · pdf · doi:10.48550/arxiv.1705.05915
openalex publication_date 2017/05/16 · openalex created_date 2017/05/26 · openalex updated_date 2026/07/28
We investigate a mixed 0-1 conic quadratic optimization problem with indicator variables arising in mean-risk optimization. The indicator variables are often used to model non-convexities such as fixed charges or cardinality constraints. Observing that the problem reduces to a submodular function minimization for its binary restriction, we derive three classes of strong convex valid inequalities by lifting the polymatroid inequalities on the binary variables. Computational experiments demonstrate the effectiveness of the inequalities in strengthening the convex relaxations and, thereby, improving the solution times for mean-risk problems with fixed charges and cardinality constraints significantly.