Back to Search Start Over

PARABOLIC OPTIMAL CONTROL PROBLEMS WITH COMBINATORIAL SWITCHING CONSTRAINTS, PART II: OUTER APPROXIMATION ALGORITHM.

Authors :
BUCHHEIM, CHRISTOPH
GRÜTERING, ALEXANDRA
MEYER, CHRISTIAN
Source :
SIAM Journal on Optimization; 2024, Vol. 34 Issue 2, p1295-1315, 21p
Publication Year :
2024

Abstract

We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon; they can thus be seen as dynamic switches. The switching patterns may be sub ject to combinatorial constraints such as, e.g., an upper bound on the total number of switchings or a lower bound on the time between two switchings. In a companion paper [C. Buchheim, A. Gruütering, and C. Meyer, SIAM J. Optim., arXiv:2203.07121, 2024], we describe the Lp -closure of the convex hull of feasible switching patterns as the intersection of convex sets derived from finite-dimensional pro jections. In this paper, the resulting outer description is used for the construction of an outer approximation algorithm in function space, whose iterates are proven to converge strongly in L² to the global minimizer of the convexified optimal control problem. The linear-quadratic subproblems arising in each iteration of the outer approximation algorithm are solved by means of a semismooth Newton method. A numerical example in two spatial dimensions illustrates the efficiency of the overall algorithm. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
10526234
Volume :
34
Issue :
2
Database :
Complementary Index
Journal :
SIAM Journal on Optimization
Publication Type :
Academic Journal
Accession number :
178370469
Full Text :
https://doi.org/10.1137/22M1490284