C.A. Floudas and V. Visweswaran, A global optimization algorithm (GOP) for certain classes of nonconvex NLPs: I. Theory, Comput. chem. engng., 14(12):1397, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....example in the literature due to the importance of the dehydration of ethanol using benzene as an entrainer. Kovach and Seider (1983) used the UNIQUAC equation to model this azeotropic distillation tower. The authors reported multiple steady states for this column. This system was also studied by Cairns and Furzer (1990) who emphasize the importance of modeling the third liquid phase in the column. In fact, they found that the two phase solution associated with the column actually led to the prediction of infeasible temperatures at the top of the tower. This emphasizes the need for reliable prediction of phase ....

C.A. Floudas and V. Visweswaran. A global optimization algorithm (GOP) for certain classes of nonconvex NLPs: I. Theory. Comput. chem. engng., 14(12):1397, 1990.

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C.A. Floudas and V. Visweswaran, A global optimization algorithm (GOP) for certain classes of nonconvex NLPs: I. Theory, Comput. chem. engng., 14(12):1397, 1990.

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C.A. Floudas and V. Visweswaran. A global optimization algorithm (GOP) for certain classes of nonconvex NLPs: I. Theory. Comput. chem. engng., 14(12):1397, 1990.

....the X variables form a square set of equality constraints so that (P) is simply a function evaluation. 3.4 The Relaxed Dual Problem The primal problem yields an upper bound on the global solution. The relaxed dual subproblems will yield valid lower bounds. A more detailed treatment of the theory can be found in Floudas and Visweswaran (1990, 1993) and in McDonald and Floudas (1994a) 3.4.1 Formulation of the Lagrange function The Lagrange function for use in the relaxed dual problem will supply underestimators of the Gibbs surface in partitions of the feasible region. If the following steps are performed: i) Construct the ....

C.A. Floudas and V. Visweswaran. A global optimization algorithm (GOP) for certain classes of nonconvex NLPs: I. Theory. Comput. chem. engng., 14(12):1397, 1990.

....optimization framework. A number of interesting properties are described which drastically alter the structure of the respective problems. For the NRTL equation, it is shown that the formulation can be converted into a biconvex optimization problem. The GOP algorithm of Floudas and Visweswaran [8, 9] can then be used to obtain ffl global solutions in this case. For the UNIQUAC equation, the new properties show how the objective function can be transformed into the difference of two convex functions (i.e. a D.C. programming problem is obtained) where the concave portion is separable. A ....

....for the NRTL equation can be transformed from its original nonconvex form into an optimization problem where a biconvex objective function is minimized subject to a bilinear set of constraints. This induced special structure allows the Global OPtimization (GOP) algorithm of Floudas and Visweswaran [8, 9] to be used to obtain global solutions to this problem. Next, the structure of the UNIQUAC equation is examined in detail. Two important properties are introduced which simplify the Gibbs energy expression, but still leave it in a nonconvex form. Additionally, some manipulation of terms reveal how ....

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C.A. Floudas and V. Visweswaran. A global optimization algorithm (GOP) for certain classes of nonconvex NLPs: I. Theory. Comput. chem. engng., 14(12):1397, 1990.

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Floudas, C.A., and Visweswaran, V., A Global Optimization Algorithm (GOP) for Certain Classes of Nonconvex NLPs : I. Theory, Submitted For Publication.

.... tangent plane distance is found, these solutions are used as a starting point for a search for a new equilibrium solution which will have a lower Gibbs free energy value, the assumption being that the equilibrium mol fractions will be closely approximated by the solution of (S) see, for example, Cairns and Furzer, 1990). However there is no guarantee that the correct equilibrium solution will be obtained using this starting point. In addition, even if an improved solution is found, then there is still no guarantee that this is the true global solution. The approach of Michelsen (1982b) uses a descent method for ....

C.A. Floudas and V. Visweswaran. A global optimization algorithm (GOP) for certain classes of nonconvex NLPs: I. Theory. Comput. chem. engng., 14(12):1397, 1990.

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C. A. Floudas and V. Visweswaran. A global optimization algorithm (GOP) for certain classes of nonconvex NLPs: I. theory. C&ChE, 14:1397, 1990.

....it possible to tackle with substantial efficiency otherwise intractable global optimization problems. In this paper, we will discuss implementation issues and computational results associated with the distributed implementation of the decomposition based global optimization algorithm, GOP, 5] [6]. The NP complete character of the global optimization problem, translated into extremely high computational requirements, had made it difficult to address problems of large size.The parallel implementation made it possible to successfully tackle the increased computational requirements in in ....

.... [15] Outer Approximation methods [10] Reformulation Linearization methods [14] Interval methods, 8] The probabilistic methods include among others : Random Searches, 11] Clustering methods, 13] Recently, a deterministic primal relaxed dual global optimization method was proposed [5] [6], 17] for certain classes of nonconvex optimization problems. Employing duality theory, a global optimization algorithm, GOP, was developed. Through a series of primal and relaxed dual problems, that provide valid upper and lower bounds on the global solution, the global minimum is identified. ....

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C. A. Floudas and V. Visweswaran. A Global Optimization Algorithm (GOP) for Certain Classes of NonconvexNLPs: I. Theory. Comp. chem. Eng., 14:1397--1417, 1990.

....A. FLOUDAS envelope described in [2] provides the desired underestimator. For concave functions, linearization generates the tightest lower bound. Convex underestimators for several special classes of functions, such as biconvex, fractional, trilinear and signomial terms have also been developed [7], 8] 16] 22] 23] In the case of an arbitrary nonconvex function, the use of a convex underestimator based on second order information was suggested in [3] It was incorporated in a branch and bound algorithm, the ffBB, which is based on a difference of convex functions transformation and ....

C. A Floudas and V. Visweswaran, A Global Optimization Algorithm (GOP) for Certain Classes of Nonconvex NLPs : I. Theory, Comp. Chem. Engng., 14:1397--1417, 1990.

....nonconvex functions involved. Successive improvements of these estimates, together with the identification of the global solution of the resulting convex programs, eventually lead to the determination of the global optimal solution of the original nonconvex problem. The GOP algorithm developed by Floudas and Visweswaran (1990, 1993, see also Visweswaran and Floudas, 1990, 1993, 1996a,b) is an instance of a decomposition method in which the special structure of the problem is exploited in order to construct valid underestimators. The branch and bound algorithm of Al Khayyal and Falk (1983) takes advantage of the ....

....estimates, together with the identification of the global solution of the resulting convex programs, eventually lead to the determination of the global optimal solution of the original nonconvex problem. The GOP algorithm developed by Floudas and Visweswaran (1990, 1993, see also Visweswaran and Floudas, 1990, 1993, 1996a,b) is an instance of a decomposition method in which the special structure of the problem is exploited in order to construct valid underestimators. The branch and bound algorithm of Al Khayyal and Falk (1983) takes advantage of the properties of bilinear functions for which the ....

C. A. Floudas and V. Visweswaran. A Global Optimization Algorithm (GOP) for Certain Classes of Nonconvex NLPs : I. Theory. Computers chem. Engng., 14:1397--1417, 1990.

....the NRTL equation is provided. It is subsequently shown that by introducing new variables, the problem can then be transformed into one where a biconvex objective function is minimized over a set of bilinear constraints. Secondly, the Global OPtimization (GOP) algorithm (Floudas and Visweswaran, [13, 14]; Visweswaran and Floudas, 60, 61, 62] is used to exploit these induced properties of the formulation to guarantee convergence to an ffl global solution, regardless of the starting point. A geometrical interpretation is provided for a selected smaller, but challenging, example. Numerous examples ....

....of composition. In the following section, the requisite thermodynamic background for the phase and chemical equilibrium problem is provided, describing the assumptions that are made in this work. Then, a general description of the Global OPtimization algorithm (GOP) of Floudas and Visweswaran [13, 14] is given, outlining the required structure that a problem must possess in order to apply it. The Gibbs free energy expression is analyzed in detail. An important property that simplifies the objective function considerably is introduced. Then, it is described how new transformation variables are ....

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C.A. Floudas and V. Visweswaran, A global optimization algorithm (GOP) for certain classes of nonconvex NLPs: I. Theory, Comput. chem. engng., 14(12):1397, 1990.

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C. A. Floudas and V. Visweswaran. A global optimization algorithm (GOP) for certain classes of nonconvex NLPs: I. theory. Comp. & Chem. Eng., 14:1397, 1990.

....techniques cannot guarantee that the global solution will be found due to the presence of the nonconvex horizon constraints. This suggests that global optimization techniques must be developed to solve these problems. Ierapetritou and Pistikopoulos (1995) 1996) applied the GOP algorithm of Floudas and Visweswaran (1990), 1993) for the case of a fixed number of equipment units per stage with relaxation constraint (6) In the following section, a very important theoretical property will be presented which allows very tight bounds on the global solution to be obtained in a small number of iterations. 3 Lower ....

Floudas, C. A., and Visweswaran, V. A Global Optimization Algorithm (GOP) for Certain Classes of Nonconvex NLPs : I. Theory. Comp. Chem. Engng., 14:1397--1417, 1990.

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Floudas, C.A. and V. Visweswaran (1990). A Global Optimization Algorithm (GOP) for Certain Classes of Nonconvex NLPs-I. Theory. Comput. Chem. Engng., 14, 1397.

....and stochastic. The deterministic approaches include Lipschitzian methods [12] 13] branch and bound procedures [2] 15] 1] cutting plane methods [32] difference of convex functions and reverse convex methods [31] outer approximation approaches [14] primal dual methods [29] [6], 7] 33] 4] reformulation linearization [27] 28] and interval methods [8] Stochastic approaches, encompass among others simulated annealing [26] genetic algorithms [10] 3] and clustering methods [25] A number of books [23] 30] 24] 16] 5] 11] summarize the latest ....

....multiple local and disconnected feasible regions. It has been observed in practice that existing path following techniques cannot consistently locate the global minimum solution of (P0) even if a multi start procedure are utilized. For special cases of (P0) involving bilinear or polynomial terms [6], 7] signomial terms [18] efficient algorithms have been proposed for locating the global minimum solution. For the general case, however, of minimizing a nonconvex function subject to a set of nonconvex equality and inequality constraints there has been comparatively little work in deriving ....

C.A. Floudas and V. Visweswaran. A global optimization algorithm (GOP) for certain classes of nonconvex NLPs: I. Theory. Comput. chem. Engng., 14(12):1397, 1990.

....In this section, we describe some interesting problems in mathematicalprogramming, engineering design and control that can be formulated as quadratic programming problems. Several applications and test problems for quadratic programming, as well as general nonconvex optimization problems can be found in Floudas and Pardalos (1990). 10.1. Economies of Scale Problems involving economies of scale (in production and sales) often can be formulated as concave quadratic programming problems. Consider a case when n products are being produced, with x i being the number of units of product i and c i being the cost of production ....

C.A. Floudas and V. Visweswaran. A Global Optimization Algorithm (GOP) for Certain Classes of Nonconvex NLPs: I. Theory. Comp. &Chem. Eng., 14:1397--1417, 1990.

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V. Visweswaran and C.A. Floudas (1990). A Global Optimization Algorithm (GOP) for Certain Classes of Nonconvex NLP's II, Application of Theory and Test Problems, Computers Chem. Eng., 14 (12), 1417--1434.

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V. Visweswaran and C.A. Floudas (1990). A Global Optimization Algorithm (GOP) for Certain Classes of Nonconvex NLP's II, Application of Theory and Test Problems, Computers Chem. Eng., 14 (12), 1417--1434.

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