(448a) Easy Advanced Global Optimization (EAGO): An Open-Source Platform for Robust and Global Optimization in Julia

The use of generalized McCormick relaxations in global optimization problems presents significant advantages in process systems engineering applications.. These include the generation of tight relaxations and quadratically-convergent iterative methods which help to avoid clustering. Additionally, problems may even be solved with a reduction in dimensionality, in contrast to the state of the art auxiliary-variable-methods (AVM) [1-4].

However, the usage of these techniques has been limited due to: the need to utilize a non-smooth solver, complexity in formulating relaxations of implicit functions, and the necessity of object-oriented programming approaches [1,2]. These object-oriented approaches have previously required a trade-off between accessibility and speed. Favoring performance, current implementations are available in C++ [1,2,6-8] which makes accessibility an issue as higher-level programming languages, such as MATLAB® [5], have come to predominate end-user applications.

The first limitation has recently been eliminated by a novel method for constructing differentiable relaxations [6]. Implicit function theory has recently been advanced within a generalized McCormick relaxation framework for addressing global optimization problems in reduced space [7,8]. In this paper, we address the third major limitation by introducing an easy advanced global optimization (EAGO) package for Julia [9].

As a Julia implementation, EAGO offers a user-friendly front-end while maintaining speed comparable to the C language. This software package makes use of modern techniques in McCormick-type relaxations and validated interval arithmetic to solve globally nonlinear optimization problems with a guaranteed certificate of optimality. The package contains three main components:

• C1) Routines which make use of differentiable and implicit McCormick-based relaxation theory to solve optimization problems efficiently in reduced space.
• C2) Implementations of meta-algorithms for the solution of nonconvex semi-infinite programs (SIP) are also made available in this package [7,10]. The routine can be utilized with user-specified solvers such as BARON [3-4] in additional to the provided global optimization library. 
• C3) Also included in the software package are Julia implementations of extended-interval arithmetic, McCormick-relaxations (both standard and differentiable), reverse-interval propagation via computational graphs, and a branch & bound library.

This paper will focus on demonstrating the capabilities of EAGO. Use-cases for SIP meta-algorithms will be provided to demonstrate the ease with which robust optimization problems may be formulated and efficiently solved. Additional examples will be given illustrating the application of EAGO solvers to large systems that commonly arise in model-based system engineering applications. Benchmark results will be provided and compared to state-of-the-art optimization software (BARON [3-4], ANTIGONE [12]) based on select samples from the COCONUT library [11]. Industrially-relevant process systems engineering examples will be presented illustrating both ease-of-use and performance aspects of EAGO.

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[5] MATLAB version 9.0.0. Natick, Massachusetts: The MathWorks Inc., 2016

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[11] O. Shcherbina, et al. Benchmarking Global Optimization and Constraint Satisfaction Codes, In Global Optimization and Constraint Satisfaction, Bliek, Ch., Jermann, Ch. and Neumaier, A. Springer, Berlin 2003, 212-222.

[12] Misener, R. and Floudas, C.A. ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations. J Global Optim, 59:503-526, 2014.