This paper presents a canonical dual approach for finding either an optimal or approximate solution to the maximum cut problem (MAX CUT). We show that, by introducing a linear perturbation term to the objective function, the maximum cut problem is perturbed to have a dual problem which is a...

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...

This paper introduces the global mixed-integer quadratic optimizer, GloMIQO, a numerical solver addressing mixed-integer quadratically-constrained quadratic programs to <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${\varepsilon}$$</EquationSource> </InlineEquation>-global optimality. The algorithmic components are presented for: reformulating user input, detecting...</equationsource></inlineequation>

Two approaches that solve the mixed-integer nonlinear bilevel programming problem to global optimality are introduced. The first addresses problems mixed-integer nonlinear in outer variables and C <Superscript>2</Superscript>-nonlinear in inner variables. The second adresses problems with general mixed-integer nonlinear...</superscript>

This paper presents a set of complete solutions and optimality conditions for a nonconvex quadratic-exponential optimization problem. By using the canonical duality theory developed by the first author, the nonconvex primal problem in n-dimensional space can be converted into an one-dimensional...