Soft Computing

, Volume 22, Issue 10, pp 3343–3355 | Cite as

Verifiable outsourcing of constrained nonlinear programming by particle swarm optimization in cloud

  • Tao XiangEmail author
  • Weimin Zhang
  • Shigang Zhong
  • Jiyun Yang
Methodologies and Application


In this paper, we explore the verification problem of outsourcing constrained nonlinear programming (NLP) when it is required to be solved by particle swarm optimization (PSO) algorithm, i.e., making sure that the cloud runs PSO algorithm faithfully and returns an acceptable solution. An efficient verification scheme without any cryptographic tool is proposed. The proposed scheme involves approximate KKT conditions with the \(\varepsilon \)-KKT point in verifying the optimality of the result returned by PSO algorithm. Extensive experiments on PSO benchmarks and NLP test problems demonstrate that our proposed scheme is effective and efficient at verifying the cloud’s honesty.


Particle swarm optimization Verifiable outsourcing Nonlinear programming Approximate KKT conditions 



This work was supported by the National Natural Science Foundation of China (No. 61672118) and the Fundamental Research Funds for the Central Universities (No. 106112016CDJZR185513).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Tao Xiang
    • 1
    Email author
  • Weimin Zhang
    • 1
  • Shigang Zhong
    • 1
  • Jiyun Yang
    • 1
  1. 1.College of Computer ScienceChongqing UniversityChongqingChina

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