In comparison to other energy storage systems, Liquid Air Energy Storage (LAES) technology offers a number of advantages, including high energy density and scalability, cost-competitiveness and non-geographical constraints. As a result, it has attracted a growing interest in recent years. The primary objective of the current paper is to develop a computational tool for optimizing Liquid Air Energy Storage Systems (LAES). In order to achieve this, a deterministic and non-linear mathematical model has been implemented in an object-oriented equation-based programming language (GAMS), which has been solved with a derivative-based optimization algorithm based on the reduced generalized gradient. The thermodynamic properties of the process streams have been calculated from a dynamic link library (DLL) programmed in the C environment. Once the model had been successfully verified, it was used to maximize the round-trip efficiency (RTE). Compared to a base case taken from the literature, improvements in round-trip efficiency and liquid air yield were achieved simultaneously from the proposed model. As detailed models for all process units, including the modelling of the liquefaction process, were developed, these models can be combined in different ways to represent any LAES system for the purpose of optimizing any desired criteria, including maximum efficiency or minimum cost. Therefore, this work represents an advance in mathematical modelling from the Process System Engineering (PSE) perspective, demonstrating the application of simultaneous optimization, derivative-based algorithms, and rigorous property package estimation through dynamic link libraries to optimize any cryogenic air energy storage system.