Convergence of finite-dimensional approximations for mixed-integer optimization with differential equations∗
Hante F, Schmidt M (2019)
Publication Type: Journal article
Publication year: 2019
Journal
Book Volume: 48
Pages Range: 209-230
Journal Issue: 2
Abstract
We consider a direct approach to solving the mixedinteger nonlinear optimization problems with constraints depending on initial and terminal conditions of an ordinary differential equation. In order to obtain a finite-dimensional problem, the dynamics are approximated using discretization methods. In the framework of general one-step methods, we provide sufficient conditions for the convergence of this approach in the sense of the corresponding optimal values. The results are obtained by considering the discretized problem as a parametric mixed-integer nonlinear optimization problem in finite dimensions, where the step size for discretization of the dynamics is the parameter. In this setting, we prove the continuity of the optimal value function under a stability assumption for the integer feasible set and second-order conditions from nonlinear optimization. We address the necessity of the conditions on the example of pipe sizing problems for gas networks.
Authors with CRIS profile
Involved external institutions
Germany (DE)How to cite
APA:
Hante, F., & Schmidt, M. (2019). Convergence of finite-dimensional approximations for mixed-integer optimization with differential equations∗. Control and Cybernetics, 48(2), 209-230.
MLA:
Hante, Falk, and Martin Schmidt. "Convergence of finite-dimensional approximations for mixed-integer optimization with differential equations∗." Control and Cybernetics 48.2 (2019): 209-230.
BibTeX: Download