arXiv:2406.05638v1 [math.OC] 9 Jun 2024 Exponential Conic Relaxations for Signomial Geometric Programming Milad Dehghani Filabadi a , Chen Chen a,∗ a Department of Integrated Systems Engineering, The Ohio State University, Columbus, OH, USA Abstract Signomial geometric programming (SGP) is a computationally challenging, NP-Hard class of non- convex nonlinear optimization problems. SGP can be solved iteratively using a sequence of convex relaxations; consequently, the strength of such relaxations is an important factor to this iterative approach. Motivated by recent advances in solving exponential conic programming (ECP) prob- lems, this paper develops a novel convex relaxation for SGP. Unlike existing work on relaxations, the base model in this paper does not assume bounded variables. However, bounded variables or monomial terms can be used to strengthen the relaxation by means of additional valid linear in- equalities. We show how to embed the ECP relaxation in an iterative algorithm for SGP; leveraging recent advances in interior point method solvers, our computational experiments demonstrate the practical effectiveness of this approach. Keywords: global optimization, exponential conic programming, signomial geometric programming, convex relaxations, valid inequalities Declarations of interest: None 1. Introduction Signomial geometric programming (SGP) problems are optimization problems involving both positive and negative monomials in the constraints and objective function (Duffin and Peterson, 1973) (see 2 for a definition). SGP problems have wide-ranging applications including engineer- ing design (Avriel and Barrett, 1978; Marin-Sanguino et al., 2007; Xu, 2013)), inventory control (Kim and Lee, 1998; Jung and Klein, 2005; Mandal et al., 2006), gas networks (Mishra et al., 2017), project management (Scott and Jefferson, 1995), aircraft design (Kirschen et al., 2018; Ozturk and Saab, 2019), and power control (Chiang et al., 2007). SGP problems belong to a class of NP-hard (see Xu (2014)), nonconvex, nonlinear prob- lems, posing computational barriers to attaining global optimality (see, e.g. (Opgenoord et al., 2017; Murray et al., 2021)). As such, numerous local heuristic algorithms have been proposed to ∗ Corresponding author Email addresses: dehghanifilabadi.1@osu.edu (Milad Dehghani Filabadi), chen.8018@osu.edu (Chen Chen) Preprint submitted to European Journal of Operational Research June 11, 2024