Sequential Quadratic Programming SQP

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. 

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]. 

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). ... 

The Lagrange function is approximated with a quadratic function, whereas the nonlinear constraints are linearized (Sequential Quadratic Programming, SQP, method see Section 13.7). Also in this case, a lower level BzzConstrai-nedMinimization class object with a quadratic objective function and hnear constraints is invoked. 

Optimization is performed solving a Multiobjective Optimization Problem (MOP) using as optimization algorithm a customized Sequential Quadratic Programming (SQP) method (Fletcher 1987). The solution of the MOP provides the Pareto front of the problem which, in our application, consists of 155 optimal solutions. However, as inputs of the equipment reliability and cost models fluctuate according to distribution laws reflecting uncertainty on parameters, objective functions will fluctuate also in repeated runs. 

Sequential quadratic programming (SQP) methods are iterative methods that solve at the Ml iteration a quadratic sub-problem (QP) of the form QP [22, 23] ... 

OC/DO-problems can be solved very efficiently and reliably by combining the above problem discretization (piecewise control parameterization and multiple shooting state discretization) with a specifically tailored sequential quadratic programming (SQP) algorithm for the solution of the large, but structured NLP problem (2.3). Such a strategy has been implemented in the optimal control code MUSCOD [6, 13]. 

The MINLPsolver can be OAERAp based on outer proximation algorithms or SRQPD employs a sequential quadratic programming (SQP) method for the solution of the nonlinear progranuning (NLP) problem. 

Thus, the concentration of the chemical species has been determined in each of these regions. The numbers of phases and chemical species in each region have been chosen based on information reported in the literature. A Sequential Quadratic Programming (SQP) method has then been used to solve the minimisation problem. 

The augmented Lagrangian method is not the only approach to solving constrained optimization problems, yet a complete discussion of this subject is beyond the scope of this text. We briefly consider a popular, and efficient, class of methods, as it is used by fmincon, sequential quadratic programming (SQP). We wUl find it useful to introduce a common notation for the equality and inequality constraints using slack variables. 

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