- Tytuł:
- Convergence of finite-dimensional approximations for mixed-integer optimization with differential equations
- Autorzy:
-
Hante, Falk M.
Schmidt, Martin - Powiązania:
- https://bibliotekanauki.pl/articles/1839150.pdf
- Data publikacji:
- 2019
- Wydawca:
- Polska Akademia Nauk. Instytut Badań Systemowych PAN
- Tematy:
-
optimization
differential equations
optimal value function
Lipschitz continuity
parametric optimization
mixed integer nonlinear programming - Opis:
- 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.
- Źródło:
-
Control and Cybernetics; 2019, 48, 2; 209-226
0324-8569 - Pojawia się w:
- Control and Cybernetics
- Dostawca treści:
- Biblioteka Nauki
Artykuł