Improved McCormick Relaxations for the efficient Global Optimization in the Space of Degrees of Freedom

该项目的目标是为确定性全局优化问题开发一种先进的程序。我们的目标是扩展McCormicks技术的建设凸和凹松弛，以直接构造有效的仿射松弛的给定问题。我们比较新开发的方法，其他放松技术。McCormicks方法保留了原有的变量空间，而其他松弛方法则通过在松弛过程中引入辅助变量来增加自由度空间。我们期望在原始变量空间中求解仿射松弛将导致更高的计算效率，从而减少全局优化领域中基于凸松弛和凹松弛构造的算法的总计算时间。四种方法，以获得有效的仿射松弛将开发和比较，目前国家的最先进的松弛方法。为了进行比较，将在数值库中找到的给定基准案例上实现和测试所提出的想法，以进行全局优化。此外，这些想法将在创新的过程系统工程配方中进行测试。

The objective of the project is to develop an advanced procedure for deterministic global optimization problems. We aim to extend McCormicks technique for construction of convex and concave relaxations in order to directly construct valid affine relaxations of the given problem. We compare the newly developed methods to other relaxation techniques. McCormicks procedure retains the original variable space while other relaxation techniques increase the space of degrees of freedom by introducing auxiliary variables during the relaxation process. We expect that solving the affine relaxations in the original variable space will result in higher computational efficiency and thus decrease the overall computation time of algorithms based on the construction of convex and concave relaxations in the field of global optimization. Four approaches in order to obtain valid affine relaxations will be developed and compared to current state-of-the-art relaxation methods. To enable the comparison, the proposed ideas will be implemented and tested on given benchmark cases found in numerical libraries for global optimization. Furthermore, the ideas will be tested in innovative process systems engineering formulations.