Sequential quadratic

To solve the problem a sequential quadratic programming code was used in the outer loop of calculations. Inner loops were used to evaluate the physical properties. Forward-finite differences with a step size of h = 10 7 were used as substitute for the derivatives. Equilibrium data were taken from Holland (1963). The results shown in Table E12.1B were essentially the same as those obtained by Sargent and Gaminibandara. 

EXAMPLE 14.3 SOLUTION OF AN ALKYLATION PROCESS BY SEQUENTIAL QUADRATIC PROGRAMMING... 

B approximation to the Hessian matrix used in sequential quadratic pro-... 

Example 14.3 Solution of an Alkylation Process by Sequential Quadratic... 

Sequential quadratic programming. A sequential quadratic programming (SQP) technique involves the resolution of a sequence of explicit quadratic programming (QP) subproblems. The solution of each subproblem produces the search direction d that has to be taken to reach the next iterate zk+i from the current iterate zk. A one-dimensional search is then accomplished in the direction dt to obtain the optimal step size. 

The above problem becomes an NLP problem when we fix the integer variables and since we have only 10 feasible compounds, 10 NLP problems were solved by fixing the binary variables representing the 10 compounds. Sequential quadratic programming algorithm was used to solve the NLP problems. The molecular structure and design results of the optimal solvent and 2-ethoxy ethyl acetate are shown in Table 1. 

Fig. 6.7 Comparison of the maximum of the neural network approximation of the ODHE ethylene yield obtained in 10 runs of the genetic algorithm with a population size 60, and the global maximum obtained with a sequential quadratic programming method run for 15 different starting points.

Provided that the reaction kinetics are known, the available models can be used to determine optimal dosing profiles for single units and for multistage arrangements. Typical results that can be obtained by solving Eq. (48) numerically and applying a sequential quadratic programming (SQP) optimizer are shown in Fig. 12.18 [66]. 

Keywords Real-time Optimization, Genetic Algorithm, Sequential Quadratic Programming, Hybrid Algorithms, Hydrogenation Reactors. 

Solution methods for optimization problems that involve only continuous variables can be divided into two broad classes derivative-free methods (e.g., pattern search and stochastic search methods) and derivative-based methods (e.g., barrier function techniques and sequential quadratic programming). Because the optimization problems of concern in RTO are typically of reasonably large scale, must be solved on-line in relatively small amounts of time and derivative-free methods, and generally have much higher computational requirements than derivative-based methods, the solvers contained in most RTO systems use derivative-based techniques. Note that in these solvers the first derivatives are evaluated analytically and the second derivatives are approximated by various updating techniques (e.g., BFGS update). 

RTO was based on solvers such as MINOS, which uses a reduced Lagrangian approach, most solvers used for RTO are based on sequential quadratic programming (SQP). ... 

Problem Type Smooth nonlinear functions subject to smooth constraints Method Sequential quadratic programming Author Peter SpeUucci, Technical University Darmstadt, Germany Contact http //www.mathematik.tu-darmstadt.de/ags/ag8/spellucci/... 

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