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首页> 外文期刊>RAIRO Operation Research >CONVEX QUADRATIC UNDERESTIMATION AND BRANCH AND BOUND FOR UNIVARIATE GLOBAL OPTIMIZATION WITH ONE NONCONVEX CONSTRAINT
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CONVEX QUADRATIC UNDERESTIMATION AND BRANCH AND BOUND FOR UNIVARIATE GLOBAL OPTIMIZATION WITH ONE NONCONVEX CONSTRAINT

机译：具有一个非凸约束的全局全局优化的凸二次方低估和分支与界

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摘要

The purpose of this paper is to demonstrate that, for globally minimize one dimensional nonconvex problems with both twice differentiable function and constraint, we can propose an efficient algorithm based on Branch and Bound techniques. The method is first displayed in the simple case with an interval constraint. The extension is displayed afterwards to the general case with an additional nonconvex twice differentiable constraint. A quadratic bounding function which is better than the well known linear underestimator is proposed while w-subdivision is added to support the branching procedure. Computational results on several and various types of functions show the efficiency of our algorithms and their superiority with respect to the existing methods.
机译：本文的目的是证明，为了全局地最小化具有两次可微函数和约束的一维非凸问题，我们可以提出一种基于Branch and Bound技术的有效算法。该方法首先在具有间隔约束的简单情况下显示。扩展名随后显示给一般情况，并带有一个附加的非凸两次可微约束。当添加w细分以支持分支过程时，提出了一种优于公知的线性低估器的二次边界函数。几种不同类型函数的计算结果表明了我们算法的效率及其相对于现有方法的优越性。

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