Many real-world applications can usually be modeled as convex quadratic problems. In the present paper, we want to tackle a specific class of quadratic programs having a dense Hessian matrix and a structured feasible set. We hence carefully analyze a simplicial decomposition like algorithmic framework that handles those problems in an effective way. We introduce a new master solver, called Adaptive Conjugate Direction Method, and embed it in our framework. We also analyze the interaction of some techniques for speeding up the solution of the pricing problem. We report extensive numerical experiments based on a benchmark of almost 1400 instances from specific and generic quadratic problems. We show the efficiency and robustness of the method when compared to a commercial solver (Cplex).

中文翻译：

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基于共轭方向的简单分解框架，用于求解一类特定的密集凸二次程序

通常可以将许多实际应用程序建模为凸二次问题。在本文中，我们要解决一类特定的二次程序，该程序具有密集的Hessian矩阵和结构化的可行集。因此，我们仔细分析了像算法框架这样的简单分解，它可以有效地处理这些问题。我们引入了一个新的主求解器，称为自适应共轭方向法，并将其嵌入到我们的框架中。我们还分析了一些技术的相互作用，以加快定价问题的解决速度。我们报告了基于特定和通用二次问题的近1400个实例的基准进行的大量数值实验。与商用求解器（Cplex）相比，我们展示了该方法的效率和鲁棒性。