8 papers
On convergence of solutions to nonlocal optimal control problems with quasi-minimization constraints
Joshua M. Siktar
This paper studies a new class of nonlocal optimal control problems where the constraints involve approximations of minimizers of quasiconvex energies. These problems are parameter…
A Mountain-Pass Algorithm for Nonlocal Problems with Super-quadratic Nonlinearities
Loic Cappanera, Gabriela Jaramillo, Joshua M. Siktar
In this paper we consider a nonlinear equation with a super-quadratic nonlinearity, , and a nonlocal operator, , generated by a spe…
Localization for nonlocal gradient-based optimal control problems
Javier Cueto, Joshua M. Siktar
In this paper we consider optimal control problems in the nonlocal function space framework of Bellido-2023, where there are two different parameters: a horizon parameter ;…
Alleviating missing boundary conditions in elliptic partial differential equations using interior point measurements
Andrea Bonito, Alan Demlow, Joshua M. Siktar
We consider an optimal recovery problem for the Poisson problem when the boundary data is unknown. Compensating information is provided in the form of a finite number of measuremen…
-convergence of an Enhanced Finite Element Method for Manià 's and Foss's Problems Exhibiting the Lavrentiev Gap Phenomenon
Xiaobing Feng, Joshua M. Siktar
It is well-known that numerically approximating calculus of variations problems possessing a Lavrentiev Gap Phenomenon (LGP) is challenging, and the standard numerical methodologie…
Asymptotic compatibility of parametrized optimal design problems
Tadele Mengesha, Abner J. Salgado, Joshua M. Siktar
We study optimal design problems where the design corresponds to a coefficient in the principal part of the state equation. The state equation, in addition, is parameter dependent,…