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A Global Optimization Method, αBB, for General TwiceDifferentiable Constrained NLPs: I  Theoretical Advances
, 1997
"... In this paper, the deterministic global optimization algorithm, αBB, (αbased Branch and Bound) is presented. This algorithm offers mathematical guarantees for convergence to a point arbitrarily close to the global minimum for the large class of twicedifferentiable NLPs. The key idea is the constru ..."
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Cited by 51 (3 self)
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In this paper, the deterministic global optimization algorithm, αBB, (αbased Branch and Bound) is presented. This algorithm offers mathematical guarantees for convergence to a point arbitrarily close to the global minimum for the large class of twicedifferentiable NLPs. The key idea is the construction of a converging sequence of upper and lower bounds on the global minimum through the convex relaxation of the original problem. This relaxation is obtained by (i) replacing all nonconvex terms of special structure (i.e., bilinear, trilinear, fractional, fractional trilinear, univariate concave) with customized tight convex lower bounding functions and (ii) by utilizing some α parameters as defined by Maranas and Floudas (1994b) to generate valid convex underestimators for nonconvex terms of generic structure. In most cases, the calculation of appropriate values for the α parameters is a challenging task. A number of approaches are proposed, which rigorously generate a set of α par...
Locating All Homogeneous Azeotropes In Multicomponent Mixtures
 IND. ENG. CHEM. RES
, 1997
"... A novel approach for enclosing all homogeneous azeotropes in multicomponent mixtures is presented. The thermodynamic criteria for azeotropy are outlined, and mathematical equations for each criterion are developed. The global optimization approach is based on developing convex underestimators which ..."
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Cited by 10 (0 self)
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A novel approach for enclosing all homogeneous azeotropes in multicomponent mixtures is presented. The thermodynamic criteria for azeotropy are outlined, and mathematical equations for each criterion are developed. The global optimization approach is based on developing convex underestimators which are coupled with a branch and bound framework in which upper and lower bounds on the solution are refined by successively partitioning the target region into small disjoint rectangles. The objective of such an approach is to enclose all global minima since each global minimum corresponds to an homogeneous azeotrope. Because of the nature of the thermodynamic equations which describe the behavior of the liquid phase, the constraint equations are highly nonlinear and nonconvex. The success of this approach depends upon constructing valid convex lower bounds for each nonconvex function in the constraints. Four different thermodynamic models are studied, the Wilson, NRTL, UNIQUAC, and UNIFAC equ...
A Global Optimization Method, αBB, for Process Design
 COMPUT. CHEM. ENG
, 1996
"... A global optimization algorithm, αBB, for twicedifferentiable NLPs is presented. It operates within a branchandbound framework and requires the construction of a convex lower bounding problem. A technique to generate such a valid convex underestimator for arbitrary twicedifferentiable functions ..."
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Cited by 7 (1 self)
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A global optimization algorithm, αBB, for twicedifferentiable NLPs is presented. It operates within a branchandbound framework and requires the construction of a convex lower bounding problem. A technique to generate such a valid convex underestimator for arbitrary twicedifferentiable functions is described. The αBB has been applied to a variety of problems and a summary of the results obtained is provided.