Parallel Secure Outsourcing of Large-scale Nonlinearly Constrained Nonlinear Programming Problems

Nonlinearly constrained nonlinear programming (NLC-NLP) problems arise in various real-world decision-making fields, such as financial engineering, urban planning, supply chain management, and power system control. They are usually large-scale because of having to consider massive variables and constraints. Solving NLC-NLP problems by employing common algorithms (e.g., gradient projection method (GPM)) is usually computationally-expensive, which challenges common organizations in solving large-scale NLC-NLP problems. To address this issue, an option is to adopt cloud computing for help. However, this raises security concerns since real-world NLC-NLP problems may carry sensitive information. Although previous secure outsourcing algorithms try to protect sensitive information, they still let cloud service tenants bear heavy computation burden. In this paper, we develop a practical secure outsourcing algorithm for using the GPM to solve large-scale NLC-NLP problems. To be more prominent, to accelerate computations and avoid possible memory overflowing, we parallelize the developed algorithm. We implement the developed algorithm on the Amazon Elastic Compute Cloud (EC2) and a laptop, and also offer extensive experiment results to show that the developed algorithm can reduce the tenant’s computing time significantly.