Xiao Zhao, Forschungszentrum Jülich, 07.2020
This code is an extension of my work at Forschungszentrum Jülich.
OCDES is a MATLAB-based tool that performs numerical integration to solve Optimization-Constrained Differential Equations (OCDE):
dx = f(x,v), x(0)=x_0, (1a)
v∈arg min_v g(x,v), (1b)
s.t.h_i(x,v)=0, i=1,…,M, (1c)
l_j(x,v)≥0, j=1,…,N. (1d)
x∈R^m and v∈R^n. f:R^m×R^n→R^m, g:R^m×R^n→R,h_i:R^m×R^n→R , l_j:R^m×R^n→R are at least second order continuously differentiable. OCDES provides efficient numerical solution of OCDE by using local optimality condition. A sequence of DAE systems are generated and classical index-1 DAE simulator is applied to solve the derived DAE systems.
Matlab, version 2014 or higher.
Matlab Symbolic Toolbox
The simulator needs Matlab environment.
Please refer to the example demo1.m. General steps of using OCDES are:
(1) Define state variables x and optimization variables v in symbolic format.
(2) Define functions f, g, h, l in symbolic format.
(3) Give initial condition x(0) and initial guess of v(0).
(4) Specify options for solving the inner NLP for initialization
opt_init.tol_act: tolerance to check active inequality constraints
opt_init.optimoptions: Optimization options, cf. MATLAB optimoptions
opt_sol.MaxNoUptActiveSet: maximum number of updating active set
opt_sol.tol_feasible: feasibility tolerance
(5) Specify options for integration
tstart: starting time of simulation
tfinal: ending time of simulation
opt_sol.integrator: Selected integration
opt_sol.opt_integrator: Integration options
(7) Call sOCDE_main.m to solve the OCDE.
Please cite [1], if you use the code.
Copyright (c) 2020: Forschungszentrum Jülich GmbH, Jülich, Germany.
Author: Xiao Zhao, Email: Xiao.Zhao@outlook.de
[1] Zhao, Ploch, Noack, Wiechert, Mitsos, von Lieres, Analysis of local well-posedness of optimization-constrained differential equations by local optimality conditions, AIChE J., DOI:10.1002/aic.16548.