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

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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.