A hybrid discretization algorithm with guaranteed feasibility for the global solution of semi-infinite programs
A hybrid discretization algorithm with guaranteed feasibility for the global solution of semi-infinite programs
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一种保证半无限规划全局解可行性的混合离散化算法
DOI：
10.1007/s10898-016-0476-7
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发表时间：
2017
影响因子：
1.8
通讯作者：
A. Mitsos
中科院分区：
文献类型：
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作者：
H. Djelassi;A. Mitsos
提出了一种基于离散化的半无限规划（SIP）全局解算法，保证在温和的假设下有限地收敛到可行的最优解。该算法基于两种现有算法的混合。第一个算法（Mitsos in Optimization 60(10–11):1291–1308, 2011）基于离散 SIP 约束右侧的限制。第二种算法（Tsoukalas 和 Rustem in Optim Lett 5(4):705–716, 2011）采用离散化预言问题和目标空间中的二分搜索。这些方法的混合产生了一种算法，该算法利用第一种方法的强收敛保证和相对严格的上界问题，同时采用从第二种方法改编的预言问题来生成廉价的下界和对第一种方法的限制的自适应更新。这些自适应更新有助于避免密集的离散化群体。该混合算法在理论上和计算上都优于其前身。在比参考文献中的假设更弱的假设下提供了有限收敛的证明。给出了已建立的 SIP 测试用例的数值结果。
A discretization-based algorithm for the global solution of semi-infinite programs (SIPs) is proposed, which is guaranteed to converge to a feasible,-optimal solution finitely under mild assumptions. The algorithm is based on the hybridization of two existing algorithms. The first algorithm (Mitsos in Optimization 60(10–11):1291–1308, 2011) is based on a restriction of the right-hand side of the constraints of a discretized SIP. The second algorithm (Tsoukalas and Rustem in Optim Lett 5(4):705–716, 2011) employs a discretized oracle problem and a binary search in the objective space. Hybridization of the approaches yields an algorithm, which leverages the strong convergence guarantees and the relatively tight upper bounding problem of the first approach while employing an oracle problem adapted from the second approach to generate cheap lower bounds and adaptive updates to the restriction of the first approach. These adaptive updates help in avoiding a dense population of the discretization. The hybrid algorithm is shown to be superior to its predecessors both theoretically and computationally. A proof of finite convergence is provided under weaker assumptions than the assumptions in the references. Numerical results from established SIP test cases are presented.
设计中心的半无限方法
DOI：
--
发表时间：
2006
期刊：
影响因子：
--
作者：
O. Stein
通讯作者：
O. Stein