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

Abstract

Nonlinearly constrained nonlinear programming (NLC-NLP) problems arise in various optimal decision-making fields, such as financial engineering, urban planning, supply chain management, and power system control. These real-world NLC-NLP problems are usually large-scale because they need to take into account massive variables and constraints. Solving NLC-NLP problems with common algorithms, e.g., the gradient projection method (GPM), generally incurs very high time complexity. This results in the inevitable inability of solving large-scale NLC-NLP problems by using general-purpose computers within a feasible time. To address this challenge, a cost-effective solution is to adopt cloud computing, but this raises security concerns since real-world NLC-NLP problems always carry sensitive information. Previous secure outsourcing algorithms try to protect sensitive information, but still let cloud service tenants bear heavy computation workload. To fill the gap, we develop a practical secure outsourcing algorithm for solving large-scale NLC-NLP problems with the GPM. To be more prominent, we also parallelize the secure outsourcing algorithm for accelerating computations and avoiding possible memory overflowing. We implement the proposed algorithm on the Amazon Elastic Compute Cloud (EC2) and a laptop, and notice that it can significantly reduce the tenant's computing time even for large-scale NLC-NLP problems.