abstract 98

Bulletin of Computational Applied Mathematics (Bull CompAMa) 

98

A comparison of algorithms for solving elliptic optimal control problems with nonconvex Lq-quasinorm cost (Research Paper)

Pedro Merino, Diego Vargas.

In this paper, we address the numerical solution of optimal control problems governed by elliptic partial differential equations which contain $L^q$-quasinorms (q in (0,1)) in the cost function. The nonconvexity and nonsmoothness of the quasinorm penalizers imply that the optimality conditions involves poinwise relations characterizing optimal controls. Therefore, we discuss the application of the Sequential Quadratic Hamiltonian method and its comparison with state-of-the-art algorithms for solving this class of problems.

Keywords: Nonconvex; nonsmooth; optimal control; Sequential Quadratic Hamiltonian.

Cite this paper:

Merino P., Vargas D.

A comparison of algorithms for solving elliptic optimal control problems with nonconvex Lq-quasinorm cost. 

Bull. Comput. Appl. Math. (Bull CompAMa), 

Vol. 12, No.2 pp.xx-xx, 2024.