Simultaneous strategies

Tjoa, I., and Biegler, L. (1991), Simultaneous strategies for data reconciliation and gross error detection of nonlinear systems. Comput. Chem. Eng. 15,679. 

Tjoa and Biegler (1991) used this formulation within a simultaneous strategy for data reconciliation and gross error detection on nonlinear systems. Albuquerque and Biegler (1996) used the same approach within the context of solving an error-in-all-variable-parameter estimation problem constrained by differential and algebraic equations. 

In contrast to the sequential solution method, the simultaneous strategy solves the dynamic process model and the optimization problem at one step. This avoids solving the model equations at each iteration in the optimization algorithm as in the sequential approach. In this approach, the dynamic process model constraints in the optimal control problem are transformed to a set of algebraic equations which is treated as equality constraints in NLP problem [20], To apply the simultaneous strategy, both state and control variable profiles are discretized by approximating functions and treated as the decision variables in optimization algorithms. 

The relative proportions of the separated diastereoisomers 40a and 40b (Ri = N02, R2 = CH3), the only bis-TB derivatives prepared via both synthetic pathways (Scheme 8), were not identical in each of the methods. The step-by-step synthetic approach (01JOC1607) afforded a 4 1 mixture of isomers 40a and 40b. However, in the case of the simultaneous strategy (04EJ01097), a 1 1 mixture of isomers 40a and 40b was formed under reaction conditions nearly identical to those of the cyclization method. Only the anti diastereoisomer 40b was isolated when the reaction temperature was reduced from 90 to 50°C. This difference in stereoselectivity during the formation of 40 (R3 = N02, R2 = CH3) via similar reactions can only be explained by stereoinduction of by-products, because in the reaction mixture the diastereoisomers 40a and 40b are in thermodynamic equilibrium due to the ready interconversion (racemization) of the methanodiazocine bridges in acidic media. 

Vasantharajan, S., and Biegler, L. T. "Simultaneous Strategies for Optimisation of Differential-Algebraic Systems with Enforcement of Error Criteria," Compul, Chem. Eng. 14, 1083-1100... 

Strategies used for optimization of selectivity can basically be divided into three separate groups (a) the simultaneous strategy, (b) the sequential strategy, and (c) the interpretative strategy. 

For these reasons, multivariate approaches seem better. The multivariate approaches, the topic of this chapter, can be further divided into sequential and simultaneous strategies (7-9). In sequential optimization strategies, initially only a few experiments are performed and their results are used to define the next experiment(s) (7, 8,10). In simultaneous approaches, a predefined number of experiments are performed according to a well-defined experimen-... 

I.B. Tjoa, L.T. Biegler, Simultaneous Strategies for Data Reconciliation and Gross Error Detection of Nonlinear Systems, Computer Chemical Engineering, 15 (1991), 679. 

With simultaneous strategies, the relationship between responses and factors is studied by ruiming an experimental design. 

There are two main multivariate optimization strategies sequential and simultaneous. In a simultaneous strategy a certain number of experiments defined according to an experimental design, such as a factorial or mixture design, are carried out. The experimental results are then used to obtain models (see equations 2-4 in Section 1.3) from which the optima Can be derived. 

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