Abstract
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.
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Chang, M.H., Park, Y.C. & Lee, TY. A new global optimization method for univariate constrained twice-differentiable NLP problems. J Glob Optim 39, 79–100 (2007). https://doi.org/10.1007/s10898-006-9121-1
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DOI: https://doi.org/10.1007/s10898-006-9121-1