NLP Optimisation Problem

The optimisation problem presented in the previous section can be written more formally as Find the set of decision variables, y (given by Equation 5.7) which will 

This constrained nonlinear optimisation problem can be solved using a Successive Quadratic Programming (SQP) algorithm. In the SQP, at each iteration of optimisation a quadratic program (QP) is formed by using a local quadratic approximation to the objective function and a linear approximation to the nonlinear constraints. The resulting QP problem is solved to determine the search direction and with this direction, the next step length of the decision variable is specified. See Chen (1988) for further details. 

NLP Based Dynamic Optimisation Problem- Infeasible Path Approach 

In this approach the set of DAEs presented in Equation 5.4 is discretised into a set of Algebraic Equations (AEs) by applying collocation method. 

Cuthrell and Biegler (1989) considered the orthogonal collocation method which is described below. Two Lagrange polynomials one for the state variable (x) and one for the control variable (u) can be written as  

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In the NLP optimisation problem presented in section 5.7.2, the model equations (equality constraints) can now be replaced by a set of discrete AEs. Once... 

A NLP optimisation problem can be viewed as the minimisation of an objective function F(d,x) in a design space d subject to equality c(x)a.n inequality g(x) constraints. Mathematically, the formulation is ... 

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