ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations

This manuscript introduces ANTIGONE, Algorithms for coNTinuous/Integer Global Optimization of Nonlinear Equations, a general mixed-integer nonlinear global optimization framework. ANTIGONE is the evolution of the Global Mixed-Integer Quadratic Optimizer, GloMIQO, to general nonconvex terms. The purpose of this paper is to show how the extensible structure of ANTIGONE realizes our previously-proposed mixed-integer quadratically-constrained quadratic program and mixed-integer signomial optimization computational frameworks. To demonstrate the capacity of ANTIGONE, this paper presents computational results on a test suite of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$2{,}571$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mn>2</mn> <mo>,</mo> <mn>571</mn> </mrow> </math> </EquationSource> </InlineEquation> problems from standard libraries and the open literature; we compare ANTIGONE to other state-of-the-art global optimization solvers. Copyright Springer Science+Business Media New York 2014