In this work, we propose an algorithm for finding an approximate global minimum of a concave quadratic function with a negative semi-definite matrix, subject to linear equality and inequality constraints, where the variables are bounded with finite or infinite bounds. The proposed algorithm starts with an initial extreme point, then it moves from the current extreme point to a new one with a better objective function value. The passage from one basic feasible solution to a new one is done by the construction of certain approximation sets and solving a sequence of linear programming problems. In order to compare our algorithm with the existing approaches, we have developed an implementation with MATLAB and conducted numerical experiments on numerous collections of test problems. The obtained numerical results show the accuracy and the efficiency of our approach.

中文翻译：

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凹二次函数全局最小化的逐次线性逼近算法

在这项工作中，我们提出了一种算法，该算法可找到带有负半定矩阵的凹二次函数的近似全局最小值，该算法受线性等式和不等式约束的约束，其中变量以有限或无穷大为界。所提出的算法从一个初始极限点开始，然后从当前极限点移动到具有更好目标函数值的新极限点。从一个基本可行解到一个新的可行解，是通过构造某些近似集并解决一系列线性规划问题来完成的。为了将我们的算法与现有方法进行比较，我们开发了一种使用MATLAB的实现，并对众多测试问题进行了数值实验。