Journal of Global Optimization

, Volume 39, Issue 1, pp 79–100 | Cite as

A new global optimization method for univariate constrained twice-differentiable NLP problems

Original Paper


In this paper, a new global optimization method is proposed for an optimization problem with twice-differentiable objective and constraint functions of a single variable. The method employs a difference of convex underestimator and a convex cut function, where the former is a continuous piecewise concave quadratic function, and the latter is a convex quadratic function. The main objectives of this research are to determine a quadratic concave underestimator that does not need an iterative local optimizer to determine the lower bounding value of the objective function and to determine a convex cut function that effectively detects infeasible regions for nonconvex constraints. The proposed method is proven to have a finite ε-convergence to locate the global optimum point. The numerical experiments indicate that the proposed method competes with another covering method, the index branch-and-bound algorithm, which uses the Lipschitz constant.


Global optimization Difference of convex underestimator Convex cut function Univariate NLP 


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Min Ho Chang
    • 1
  • Young Cheol Park
    • 1
  • Tai-Yong Lee
    • 1
  1. 1.Department of Chemical and Biomolecular EngineeringKorea Advanced Institute of Science and TechnologyDaejeonSouth Korea

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