Abstract

. A new approach is proposed for finding all ffl--feasible solutions for certain classes of nonlinearly constrained systems of equations. By introducing slack variables, the initial problem is transformed into a global optimization problem(P) whose multiple global minimum solutionswith a zero objectivevalue (if any)correspond to all solutionsof the initial constrainedsystem of equalities. All ffl--globally optimal points of (P) are then localized within a set of arbitrarily small disjoint rectangles. This is based on a branch and bound type global optimization algorithm which attains finite ffl--convergence to each of the multiple global minima of (P) through the successive refinement of a convexrelaxation of the feasible region and the subsequent solution of a series of nonlinear convex optimization problems. Based on the form of the participating functions, a number of techniques for constructing this convex relaxation are proposed. By taking advantage of the properties of products o...

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