Generalized Benders Decomposition for one Class of MINLPs with Vector Conic Constraint
Generalized Benders Decomposition for one Class of MINLPs with Vector Conic Constraint
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DOI：
10.1137/140967519
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发表时间：
2015-06
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通讯作者：
Zhou Wei;M. Ali
中科院分区：
文献类型：
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作者：
Zhou Wei;M. Ali
在本文中，我们主要研究一类Banach空间中带有向量圆锥约束的混合整数非线性规划问题（MINLP）。深入研究了应用于此类 MINLP 的凸向量优化问题的对偶理论。借助对偶性，我们使用广义 Benders 分解方法建立了求解该 MINLP 的算法。还提出了该算法的几个收敛定理。收敛定理概括并扩展了有限维空间中 MINLP 的现有结果。
In this paper, we mainly study one class of mixed-integer nonlinear programming problems (MINLPs) with vector conic constraint in Banach spaces. Duality theory of convex vector optimization problems applied to this class of MINLPs is deeply investigated. With the help of duality, we use the generalized Benders decomposition method to establish an algorithm for solving this MINLP. Several convergence theorems on the algorithm are also presented. The convergence theorems generalize and extend the existing results on MINLPs in finite dimensional spaces.