An efficient convexification method for solving generalized geometric problems

Convexification transformation is vital for solving Generalized Geometric Problems (GGP) in global optimization. Björk et al. [3] posited that transforming non-convex signomial terms in a GGP into 1-convex functions is currently the most efficient convexification technique. However, to the best of our knowledge, an efficient convexification method based on the concept of 1-convex functions has not been proposed. To address this research gap, we present a Beta method to maximally improve the efficiency of convexification based on the concept of 1-convex functions, and thereby enhance the accuracy of linearization without increasing the number of break points and binary variables in the piecewise linear function. The Beta method yields an excellent solution quality and computational efficiency. We compare its performance, with that of three existing approaches using four numerical examples. The computational results demonstrate that, in terms of solution quality and computation time, the proposed method outperforms the compared approaches.