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Optimized method

In practice, it is nontrivial to manually select the parameter values to obtain successful results. Moreover, it is not obvious how to measure the quality of the results. Therefore, a well defined performance measure and an efficient parameter optimization method are desired. [Pg.90]

In this section, we will discuss general optimization methods. Our example is the geometry optimization problem, i.e., the minimization of (q). However, the results apply to electronic optimization as well. There are a number of usefiil monographs on the minimization of continuous, differentiable fimctions m many variables [6, 7]. [Pg.2332]

The simplest smooth fiuictioii which has a local miiiimum is a quadratic. Such a function has only one, easily detemiinable stationary point. It is thus not surprising that most optimization methods try to model the unknown fiuictioii with a local quadratic approximation, in the fomi of equation (B3.5.1). [Pg.2333]

Most gradient optimization methods rely on a quadratic model of the potential surface. The minimum condition for the... [Pg.2334]

A very pedagogical, highly readable introduction to quasi-Newton optimization methods. It includes a modular system of algoritlnns in pseudo-code which should be easy to translate to popular progrannning languages like C or Fortran. [Pg.2360]

Concomitantly with the increase in hardware capabilities, better software techniques will have to be developed. It will pay us to continue to learn how nature tackles problems. Artificial neural networks are a far cry away from the capabilities of the human brain. There is a lot of room left from the information processing of the human brain in order to develop more powerful artificial neural networks. Nature has developed over millions of years efficient optimization methods for adapting to changes in the environment. The development of evolutionary and genetic algorithms will continue. [Pg.624]

Unconstrained optimization methods [W. II. Press, et. ah, Numerical Recipes The An of Scieniific Compulime.. Cambridge University Press, 1 9H6. Chapter 101 can use values of only the objective function, or of first derivatives of the objective function. second derivatives of the objective function, etc. llyperChem uses first derivative information and, in the Block Diagonal Newton-Raphson case, second derivatives for one atom at a time. TlyperChem does not use optimizers that compute the full set of second derivatives (th e Hessian ) because it is im practical to store the Hessian for mac-romoleciiles with thousands of atoms. A future release may make explicit-Hessian meth oils available for smaller molecules but at this release only methods that store the first derivative information, or the second derivatives of a single atom, are used. [Pg.303]

Schlick T 1992. Optimization Methods in Computational Chemistry. In Lipkowitz K B and D B Boyd (Editors) Reviews in Computational Chemistry Volume 3. New York. VCH Publishers, pp. 1-71. [Pg.315]

Numerous optimization methods aim at approximating the Hessian (or its inverse) in various ways. [Pg.306]

An efficient optimization method that allows several factors to be optimized at the same time. [Pg.672]

In many cases an optimized method may produce excellent results in the laboratory developing the method, but poor results in other laboratories. This is not surprising since a method is often optimized by a single analyst under an ideal set of conditions, in which the sources of reagents, equipment, and instrumentation remain the same for each trial. The procedure might also be influenced by environmental factors, such as the temperature or relative humidity in the laboratory, whose levels are not specified in the procedure and which may differ between laboratories. Finally, when optimizing a method the analyst usually takes particular care to perform the analysis in exactly the same way during every trial. [Pg.684]

The following texts and articles provide an excellent discussion of optimization methods based on searching algorithms and mathematical modeling, including a discussion of the relevant calculations. [Pg.704]

Optimization Methods for Chemists. VCH Publishers Deerfield Beach, FL, 1986. [Pg.704]

Reklaitis, G. V, A. Ravindran, and K. M. RagsdeU. Engineering Optimization Methods and Applications. Wiley, New York (1983). [Pg.424]

FIG. 3-54 Compl ex method, a pattern search optimization method. [Pg.485]

The development of micellar liquid chromatography and accumulation of numerous experimental data have given rise to the theory of chromatographic retention and optimization methods of mobile phase composition. This task has had some problems because the presence of micelles in mobile phase and its modification by organic solvent provides a great variety of solutes interactions. [Pg.45]

Alternative algorithms employ global optimization methods such as simulated annealing that can explore the set of all possible reaction pathways [35]. In the MaxFlux method it is helpful to vary the value of [3 (temperamre) that appears in the differential cost function from an initially low [3 (high temperature), where the effective surface is smooth, to a high [3 (the reaction temperature of interest), where the reaction surface is more rugged. [Pg.215]

Finding the minimum of the hybrid energy function is very complex. Similar to the protein folding problem, the number of degrees of freedom is far too large to allow a complete systematic search in all variables. Systematic search methods need to reduce the problem to a few degrees of freedom (see, e.g.. Ref. 30). Conformations of the molecule that satisfy the experimental bounds are therefore usually calculated with metric matrix distance geometry methods followed by optimization or by optimization methods alone. [Pg.257]


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A Practical Method for Clean Cycle Optimization

Accordion-optimized methods

Alignment methods optimal

Analytical methods optimization

Assignment methods, optimal

Automated method development/optimization

Box-Wilson optimization method

Calibration Characteristics and Uncertainty - Indicating Starting Points to Optimize Methods

Capillary electrophoresis optimization methods

Charging optimized methods

Chemometrical optimization methods

Complex systems stochastic optimization methods

Configuration-interaction theory optimization methods

Conjugate Descent method, optimal

Conjugate gradient method, optimal control

Conjugate gradient method, optimal control theory

Constrained optimization Lagrange multiplier method

Drug design optimization methods

Eigenvector Following optimization method

Example Optimization of Friedel-Crafts alkylation by the Basic simplex method

Experimental Optimization by the Simplex Method

Field optimized initial state method

First-order optimization method

Genetic analyses optimization methods

Geometry optimization ONIOM method

Global optimization method

Global optimization method calculations

Global optimization method potential-energy surface

Gradient optimization methods

Gradient-based optimization method

Hessian, in optimization methods

INDEX optimization methods

Interpolated optimized corrections method

Interpretive methods for selectivity optimization

Isocratic methods selectivity optimization

Iterative optimization methods —

Line Then Plane optimization method

Linear Synchronous Transit optimization method

Local optimization methods

Locally Updated Planes optimization method

Method Development and Optimization of Enantiomeric Separations Using Macrocyclic Glycopeptide Chiral Stationary Phases

Method Selection and Optimization

Method and optimization

Method development optimization

Method optimization approaches

Method optimization checked

Method optimization chemometric techniques

Method optimization experiments

Method optimization level selection

Method optimization model validation

Method optimization multicriteria decision-making methods

Method optimization parameters

Method optimization peak matching

Method optimization qualitative responses

Method optimization quantitative responses

Method optimization response surface designs

Methods of Searching for Optimal

Modified simplex optimization methods

Molecular geometries optimization methods

Monte Carlo optimization method

Multi-Objective Optimization Methods

Multiconfiguration Valence Bond Methods with Optimized Orbitals

Multifactorial Systematic Method Development and Optimization in Reversed-Phase HPLC

Multiplicative methods, lead optimization

Newton-Raphson methods optimization techniques

Nongradient methods of optimization

Numerical methods optimization

Objective function methods, optimization

Optimal Aligmnent Methods

Optimal Handling and Preservation Methods

Optimal control open loop method

Optimal control theory iterative methods

Optimal decomposition method

Optimal periodic control solution methods

Optimization Methods Involving a Generalized Form of f(y)

Optimization Methods and Programs

Optimization Methods without Derivatives

Optimization Nelder-Meade method

Optimization Traditional Methods

Optimization augmented Lagrangian method

Optimization basic principles and univariate methods

Optimization conjugate gradient method

Optimization deterministic local methods

Optimization experimental method

Optimization general methods

Optimization graphical methods

Optimization heuristic methods

Optimization indirect methods

Optimization methods

Optimization methods

Optimization methods basin hopping method

Optimization methods evolutionary strategies

Optimization methods parallel tempering

Optimization methods stochastic tunneling method

Optimization methods, deterministic

Optimization miscellaneous methods

Optimization multivariate methods

Optimization of HPLC Methods

Optimization of MIP performance through quantum chemical methods

Optimization of analytical methods

Optimization quasi-Newton methods

Optimization search methods

Optimization simplex method

Optimization techniques Simplex method

Optimization techniques conjugate gradient methods

Optimization techniques steepest descent method

Optimization triangle method

Optimization-Based Methods

Optimized Potential Method (OPM)

Optimized effective potential method

Optimized potential methods

Optimized valence configuration method

Optimizing analytical methods

Orbital-Optimized Single-Configuration Methods

Orbital-optimized multiconfiguration VB methods

Organic structures, global optimization methods

Other Operating Methods and Optimization

Overview on simulation optimization methods

Pareto-optimality method

Particle swarm optimization method

Perturbation theory optimization methods

Pharmaceuticals optimization methods

Predictive optimization method

Process optimization analytical methods

Protein folding optimization methods

Quasi-Newton methods BFGS optimization

SEC method optimization

Saddle optimization method

Scaling factor optimization method

Selectivity optimization interpretive methods

Self-consistent field method coordinate optimization

Self-consistent field method optimization

Sequence alignments optimal methods

Sequential Optimization Simplex Method

Sequential optimization methods

Shortcut Optimization Method

Simulated annealing-optimal histogram method

Simultaneous optimization method

Statistical Methods For Fermentation Optimization

Steam optimization methods

Steepest Descent optimization method

Steepest ascent, optimization method

Stepwise gradient optimization graphical method

Stochastic optimization methods

Stochastic optimization methods prediction

Summary of optimization methods

Superstructure optimization algorithmic methods

Target-specific optimization method

The Role of Selectivity in Practical Method Optimization

The optimal scale combination (OSC) method

Truncated Newton-Raphson optimization method

Trust-region Newton optimization method

Trust-region method optimization

Univariate methods optimization

Updated Hessian, in optimization methods

Variable metric optimization method

Variable-size simplex optimization method

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