AN OUTER-APPROXIMATION ALGORITHM FOR A CLASS OF MIXED-INTEGER NONLINEAR PROGRAMS
AN OUTER-APPROXIMATION ALGORITHM FOR A CLASS OF MIXED-INTEGER NONLINEAR PROGRAMS
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DOI：
10.1007/bf02592064
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发表时间：
1986-12-01
影响因子：
2.7
通讯作者：
GROSSMANN, IE
中科院分区：
文献类型：
--
作者：
DURAN, MA;GROSSMANN, IE
针对一类特殊的混合整数非线性规划问题，提出了一种外逼近算法。整数（或离散）变量的线性和涉及连续变量的非线性函数的凸性是基本数学结构的主要特征。该算法基于分解、外逼近和松弛的原理，有效地利用了问题的结构，包括求解非线性规划子问题的交替有限序列和混合整数线性主规划的松弛版本.算法的收敛性和最优性的性质，以及其实施的一般性讨论。数值结果报告的几个例子的问题，以说明在本文中提到的类的程序所提出的算法的潜力。最后，与广义Benders分解的理论比较，提出了放松的主程序预测的下界。
An outer-approximation algorithm is presented for solving mixed-integer nonlinear programming problems of a particular class. Linearity of the integer (or discrete) variables, and convexity of the nonlinear functions involving continuous variables are the main features in the underlying mathematical structure. Based on principles of decomposition, outer-approximation and relaxation, the proposed algorithm effectively exploits the structure of the problems, and consists of solving an alternating finite sequence of nonlinear programming subproblems and relaxed versions of a mixed-integer linear master program. Convergence and optimality properties of the algorithm are presented, as well as a general discussion on its implementation. Numerical results are reported for several example problems to illustrate the potential of the proposed algorithm for programs in the class addressed in this paper. Finally, a theoretical comparison with generalized Benders decomposition is presented on the lower bounds predicted by the relaxed master programs.