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A linear programming-based optimization algorithm for solving nonlinear programming problems

机译：用于解决非线性规划问题的基于线性规划的优化算法

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In this paper a linear programming-based optimization algorithm called the Sequential Cutting Plane algorithm is presented. The main features of the algorithm are described, convergence to a Karush-Kuhn-Tucker stationary point is proved and numerical experience on some well-known test sets is showed. The algorithm is based on an earlier version for convex inequality constrained problems, but here the algorithm is extended to general continuously differentiable nonlinear programming problems containing both nonlinear inequality and equality constraints. A comparison with some existing solvers shows that the algorithm is competitive with these solvers. Thus, this new method based on solving linear programming subproblems is a good alternative method for solving nonlinear programming problems efficiently. The algorithm has been used as a subsolver in a mixed integer nonlinear programming algorithm where the linear problems provide lower bounds on the optimal solutions of the nonlinear programming subproblems in the branch and bound tree for convex, inequality constrained problems.
机译：在本文中，提出了一种基于线性规划的优化算法，称为顺序切割平面算法。描述了该算法的主要特征，证明了收敛到Karush-Kuhn-Tucker固定点，并显示了一些著名测试集的数值经验。该算法基于凸不等式约束问题的较早版本，但是在这里，该算法扩展到包含非线性不等式和等式约束的一般连续可微化非线性规划问题。与一些现有求解器的比较表明，该算法在这些求解器中具有竞争力。因此，这种基于求解线性规划子问题的新方法是有效解决非线性规划问题的一种很好的替代方法。该算法已用作混合整数非线性规划算法的子求解器，其中线性问题为凸不等式约束问题的分支和界树中的非线性规划子问题的最优解提供了下界。

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