ODE Fitting Using Simple Representation
Keywords: ode fitting using simple representation cppad_ipopt_nlp purpose argument vector objective function initial condition constraint trapezoidal approximation source

| Prev | Next |  |  |  |  |  |  |

ODE Fitting Using Simple Representation
Purpose
In this section we represent the objective and constraint functions, (in the simultaneous forward and reverse optimization problem) using the simple representation in the sense of `cppad_ipopt_nlp`.
Argument Vector
The argument vector that we are optimizing with respect to ( x in cppad_ipopt_nlp ) has the following structure x = ( y 0 , ⋯ , y S ( Nz ) , a ) Note that x ∈ R S ( Nz ) + Na and y i = ( x Ny * i , … , x Ny * i + Ny - 1 ) a = ( x Ny * S ( Nz ) + Ny , … , x Ny * S ( Nz ) + Na - 1 )
Objective Function
The objective function ( fg 0 ( x ) in cppad_ipopt_nlp ) has the following representation, fg 0 ( x ) = ∑ i = 1 Nz H i ( y S ( i ) , a )
Initial Condition Constraint
For i = 1 , … , Ny , we define the component functions fg i ( x ) , and corresponding constraint equations, by 0 = fg i ( x ) = y i 0 - F i ( a )
Trapezoidal Approximation Constraint
For i = 1 , … , S ( Nz ) , and for j = 1 , … , Ny , we define the component functions fg Ny * i + j ( x ) , and corresponding constraint equations, by 0 = fg Ny * i + j = y j i - y j i -1 - [G j ( y i , a ) + G j ( y i -1 , a ) ] * t i - t i -1 2
Source
The file ipopt_nlp_ode_simple.hpp contains source code for this representation of the objective and constraints.

Input File: cppad_ipopt/example/ode2.omh