Core Concepts
The author introduces a non-convex relaxation approach for the chance-constrained binary knapsack problem, providing upper bounds as tight as other continuous relaxations. A polynomial-time algorithm is proposed to solve this relaxation efficiently.
Abstract
The content discusses a novel non-convex relaxation method for the chance-constrained binary knapsack problem. It compares this approach with other continuous relaxations, highlighting its efficiency in providing tight upper bounds. The proposed polynomial-time algorithm ensures quality solutions within short computation times.
The study showcases the importance of addressing data uncertainty in optimization problems and presents various modeling frameworks. It emphasizes the significance of efficient solution approaches for large-scale integer programs like the binary knapsack problem. The article delves into detailed comparisons of different relaxation methods and their integrality gaps, showcasing the advantages of the non-convex relaxation technique.
Overall, the research contributes valuable insights into optimization algorithms and highlights the practical implications of these methodologies in solving complex real-world problems efficiently.
Stats
Despite its non-convex nature, we show that the non-convex relaxation can be solved in polynomial time.
The CKP can be formulated as a second-order cone program known as ISP.
The CKP may seem artificial due to normality assumption on probability distribution.
The PTAS has a prohibitively large running time undesirable in practice.