Convexity and Monotonicity in Global Optimization
Convexity and Monotonicity in Global Optimization
复制标题
全局优化中的凸性和单调性
DOI：
10.1007/978-1-4613-0279-7_37
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
H. Tuy
中科院分区：
文献类型：
--
作者：
H. Tuy
凸性和单调性是全局优化的确定性方法中至关重要的两个属性。过去三十年开发的绝大多数确定性全局优化方法都是基于以某种形式利用凸性。另一方面，最近提出的单调优化理论仅基于单调性的利用。通过比较这两种方法： （差异凸）优化和 d.m. （差异单调）优化，本文重点关注使 d.m.从数字的角度来看，这种方法特别有吸引力，至少在一些重要的感兴趣的情况下是这样。早期开发的 d.m 基本算法的改进形式。提出了优化并将其应用于多项式规划，以说明新方法的广泛适用性。
Convexity and monotonicity are two properties of crucial importance in the deterministic approaches to global optimization. An overwhelming majority of deterministic global optimization methods developed over the last three decades are based on exploiting convexity in some form or another. On the other hand, a recently initiated theory of monotonic optimization is based on exploiting monotonicity solely. By drawing a parallel between the two approaches: d.c. (difference-convex) optimization and d.m. (difference-monotonic) optimization, this paper focuses on aspects which make the d.m. approach particularly attractive from a numerical point of view, at least in some important cases of interest. An improved form of an earlier developed basic algorithm for d.m. optimization is presented and applied to polynomial programming to illustrate the wide applicability of the new approach.