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...

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 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>

This paper presents some applications of the canonical dual theory in optimal control problems. The analytic solutions of several nonlinear and nonconvex problems are investigated by global optimizations. It turns out that the backward differential flow defined by the KKT equation may reach the...