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

机译:单变量约束两次可微NLP问题的一种新的全局优化方法

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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 non-convex 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.
机译:本文针对具有两个可微分目标和单个变量约束函数的优化问题,提出了一种新的全局优化方法。该方法利用凸低估量和凸切函数之差,其中前者是连续的分段凹二次函数,后者是凸二次函数。本研究的主要目标是确定不需要迭代局部优化器的二次凹形低估器,从而无需确定目标函数的下界值,并确定可有效检测非凸约束条件不可行区域的凸形割函数。所提出的方法被证明具有有限的ε收敛性来定位全局最优点。数值实验表明,所提出的方法与另一种覆盖方法,即使用Lipschitz常数的索引分支定界算法相抗衡。

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