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  • 1
    Electronic Resource
    Electronic Resource
    Free energy calculations for peptides via deterministic global optimization (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 110 (1999), S. 7491-7512 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The αBB algorithm is a deterministically based global optimization method that has been successfully used to locate the global minimum energy conformations of peptide systems. The goal of this procedure is to identify the native conformation of a given peptide by identifying the structure possessing the global minimum potential energy. However, a rigorous conformational search should locate the structure exhibiting the global minimum free energy. In this work, novel methods are developed for locating free energy global minimum conformations and clusters of peptides. These methods are based on an harmonic approximation for entropic effects, which requires the ability to generate a dense ensemble of distinct low energy local minima. Two approaches, both based on the general concepts of the αBB branch and bound framework, are used to generate these ensembles. In performing these calculations, potential-energy contributions were modeled using an all-atom force field. In addition, hydration effects were also considered by utilizing a solvent-accessible volume of hydration shell model. The free energy analysis was applied to both the unsolvated and solvated forms of met- and leu-enkephalin. It was found that both methods produce dense, Boltzmann-type, distributions of low-energy metastable states. The inclusion of entropic effects was also found to influence the prediction of free energy global minima. In addition, a statistical treatment of the thermodynamics of folding showed that the transition temperature, which signified a collapse from high energy, extended structures to a ground-statelike ensemble, could be identified. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.478652
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  • 2
    Electronic Resource
    Electronic Resource
    Locating all transition states and studying the reaction pathways of potential energy surfaces (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 110 (1999), S. 9259-9295 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We propose a new method for calculating all stationary states, including saddle points of all orders, of a potential energy surface based on the αBB deterministic branch and bound global optimization algorithm. This method is based on rigorous optimization methods and offers a theoretical guarantee of enclosing all solutions to the equation ∇V=0. We apply this method to Murrel–Sorbie analytic potential energy surfaces of HCN, HSiN, HBO, and CS2, and to the Empirical Conformational Energy Program for Peptides (ECEPP/3) potential energy surfaces of alanine, alanine dipeptide, and tetra-alanine. For alanine, alanine dipeptide, and tetra-alanine, we proceed to analyze the topography of the potential energy surface by calculating reaction pathways, transition rate matrices, time-evolution of occupation probabilities, and rate disconnectivity graphs. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.478850
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  • 3
    Electronic Resource
    Electronic Resource
    Unconstrained and constrained global optimization of polynomial functions in one variable (1992)
    Springer
    Journal of global optimization 2 (1992), S. 73-99 
    Details
    ISSN: 1573-2916
    Keywords: Global optimization ; polynomial functions ; unconstrained and constrained optimization ; the GOP algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In Floudas and Visweswaran (1990), a new global optimization algorithm (GOP) was proposed for solving constrained nonconvex problems involving quadratic and polynomial functions in the objective function and/or constraints. In this paper, the application of this algorithm to the special case of polynomial functions of one variable is discussed. The special nature of polynomial functions enables considerable simplification of the GOP algorithm. The primal problem is shown to reduce to a simple function evaluation, while the relaxed dual problem is equivalent to the simultaneous solution of two linear equations in two variables. In addition, the one-to-one correspondence between the x and y variables in the problem enables the iterative improvement of the bounds used in the relaxed dual problem. The simplified approach is illustrated through a simple example that shows the significant improvement in the underestimating function obtained from the application of the modified algorithm. The application of the algorithm to several unconstrained and constrained polynomial function problems is demonstrated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00121303
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  • 4
    Electronic Resource
    Electronic Resource
    A remark on the GOP algorithm for global optimization (1993)
    Springer
    Journal of global optimization 3 (1993), S. 519-521 
    Details
    ISSN: 1573-2916
    Keywords: GOP algorithm ; D.C. transformation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper it is shown that a large class of smooth mathematical programming problems can be converted into the standard forms to which the GOP algorithm applies.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01096418
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  • 5
    Electronic Resource
    Electronic Resource
    Primal-relaxed dual global optimization approach (1993)
    Springer
    Journal of optimization theory and applications 78 (1993), S. 187-225 
    Details
    ISSN: 1573-2878
    Keywords: Global optimization ; quadratic programming ; polynomial functions ; ∈-optimal solutions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A deterministic global optimization approach is proposed for nonconvex constrained nonlinear programming problems. Partitioning of the variables, along with the introduction of transformation variables, if necessary, converts the original problem into primal and relaxed dual subproblems that provide valid upper and lower bounds respectively on the global optimum. Theoretical properties are presented which allow for a rigorous solution of the relaxed dual problem. Proofs of ∈-finite convergence and ∈-global optimality are provided. The approach is shown to be particularly suited to (a) quadratic programming problems, (b) quadratically constrained problems, and (c) unconstrained and constrained optimization of polynomial and rational polynomial functions. The theoretical approach is illustrated through a few example problems. Finally, some further developments in the approach are briefly discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939667
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  • 6
    Electronic Resource
    Electronic Resource
    Generalized primal-relaxed dual approach for global optimization (1996)
    Springer
    Journal of optimization theory and applications 90 (1996), S. 417-434 
    Details
    ISSN: 1573-2878
    Keywords: Global optimization ; primal-relaxed dual approach ; penalty methods ; nonsmooth optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A generalized primal-relaxed dual algorithm for global optimization is proposed and its convergence is proved. The (GOP) algorithm of Floudas and Visweswaran (Refs. 1–2) is shown to be a special case of this general algorithm. Within the proposed framework, the algorithm of Floudas and Visweswaran (Refs. 1–2) is further extended to the nonsmooth case. A penalty implementation of the extended (GOP) algorithm is studied to improve its efficiency.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02190006
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  • 7
    Electronic Resource
    Electronic Resource
    New properties and computational improvement of the GOP algorithm for problems with quadratic objective functions and constraints (1993)
    Springer
    Journal of global optimization 3 (1993), S. 439-462 
    Details
    ISSN: 1573-2916
    Keywords: Global optimization ; indefinite quadratic programming quadratic constraints ; multiperiod tankage quality problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In Floudas and Visweswaran (1990, 1993), a deterministic global optimization approach was proposed for solving certain classes of nonconvex optimization problems. An algorithm, GOP, was presented for the solution of the problem through a series ofprimal andrelaxed dual problems that provide valid upper and lower bounds respectively on the global solution. The algorithm was proved to have finite convergence to an ∈-global optimum. In this paper, new theoretical properties are presented that help to enhance the computational performance of the GOP algorithm applied to problems of special structure. The effect of the new properties is illustrated through application of the GOP algorithm to a difficult indefinite quadratic problem, a multiperiod tankage quality problem that occurs frequently in the modeling of refinery processes, and a set of pooling/blending problems from the literature. In addition, extensive computational experience is reported for randomly generated concave and indefinite quadratic programming problems of different sizes. The results show that the properties help to make the algorithm computationally efficient for fairly large problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01096414
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  • 8
    Electronic Resource
    Electronic Resource
    αBB: A global optimization method for general constrained nonconvex problems (1995)
    Springer
    Journal of global optimization 7 (1995), S. 337-363 
    Details
    ISSN: 1573-2916
    Keywords: Global optimization ; constrained optimization ; convex relaxation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A branch and bound global optimization method,αBB, for general continuous optimization problems involving nonconvexities in the objective function and/or constraints is presented. The nonconvexities are categorized as being either of special structure or generic. A convex relaxation of the original nonconvex problem is obtained by (i) replacing all nonconvex terms of special structure (i.e. bilinear, fractional, signomial) with customized tight convex lower bounding functions and (ii) by utilizing the α parameter as defined in [17] to underestimate nonconvex terms of generic structure. The proposed branch and bound type algorithm attains finiteε-convergence to the global minimum through the successive subdivision of the original region and the subsequent solution of a series of nonlinear convex minimization problems. The global optimization method,αBB, is implemented in C and tested on a variety of example problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01099647
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  • 9
    Electronic Resource
    Electronic Resource
    Convergence of the (GOP) algorithm for a large class of smooth optimization problems (1995)
    Springer
    Journal of global optimization 6 (1995), S. 207-211 
    Details
    ISSN: 1573-2916
    Keywords: GOP algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper it is shown that the (GOP) algorithm is guaranteed to be convergent for a large class of smooth mathematical programming problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01096769
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  • 10
    Electronic Resource
    Electronic Resource
    Separation synthesis of multicomponent feed streams into multicomponent product streams (1987)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 33 (1987), S. 540-550 
    Details
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The synthesis problem of separation sequences that separate several multicomponent feed streams into several desired multicomponent product streams is addressed. A superstructure is proposed for this separation problem that has embedded all the alternative separation configurations of interest. This superstructure, which has as separator units the separation tasks that are defined for each separation breakpoint, involves options for series and/or parallel sequences, as well as stream splitting, mixing, and bypassing. Formulating and solving this superstructure as a nonlinear programming problem that has as unknowns the stream interconnections, results in an optimal separation sequence. This sequence, which may involve fewer separator units than those included in the superstructure, is shown to be a realistic and practical one. The synthesis approach is illustrated with four example problems.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/aic.690330403
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