[Ipopt] Numerical Approximation of Problem Functions - Gradient of objective, Jacobian of constraints and Hessian of Lagrangian

[Reid Byron]

Hello All,



I have implemented a trajectory optimizer using non-linear programming and
collocation per Hargraves and Paris’s canonical paper on the method linked
below.



I have been able to demonstrate the technique on a small scale toy problem
using the Sequential Least Squares Quadratic Programming [SLSQP ] solver
included within the scipy minimize function.



I am now in the process of selecting and integrating a more capable solver
to handle problems of greater size and complexity; to this end IPOPT looks
proven and promising.



I will be interfacing with IPOPT though C++.  My question pertains to
Section 3.2 Figure 2 Item 5 regarding the Evaluation of Problem Functions
within the Introduction to Ipopt document linked below.



In the hs071 example problem analytic expressions for the Gradient of the
objective, Jacobian of the constraints and Hessian of the Lagrangian are
derived.  Obtaining analytic expressions for these problem functions is
prohibitively difficult for the collocation method I am implementing.  I
can however approximate these quantities by finite difference.



*My question is thus – *

1.       Is it advisable to write a function which obtains the Gradient of
the objective, Jacobian of the constraints and Hessian of the Lagrangian by
finite difference

2.       Is there a utility existent in IPOPT which can obtain numerically
obtain the Gradient of the objective, Jacobian of the constraints and
Hessian of the Lagrangian for me?



Thank you for your time and assistance.



Reid





Direct Trajectory Optimization Using Nonlinear Programming and Collocation

https://www.researchgate.net/publication/230872953_Direct_Trajectory_Optimization_Using_Nonlinear_Programming_and_Collocation



Introduction to Ipopt

https://projects.coin-or.org/Ipopt/browser/stable/3.10/Ipopt/doc/documentation.pdf?format=raw
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