تقرير
Fractional, semilinear, and sparse optimal control: a priori error bounds
| العنوان: | Fractional, semilinear, and sparse optimal control: a priori error bounds |
|---|---|
| المؤلفون: | Bersetche, Francisco, Fuica, Francisco, Otarola, Enrique, Quero, Daniel |
| سنة النشر: | 2023 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Optimization and Control, Mathematics - Numerical Analysis |
| الوصف: | In this work, we use the integral definition of the fractional Laplace operator and study a sparse optimal control problem involving a fractional, semilinear, and elliptic partial differential equation as state equation; control constraints are also considered. We establish the existence of optimal solutions and first and second order optimality conditions. We also analyze regularity properties for optimal variables. We propose and analyze two finite element strategies of discretization: a fully discrete scheme, where the control variable is discretized with piecewise constant functions, and a semidiscrete scheme, where the control variable is not discretized. For both discretization schemes, we analyze convergence properties and a priori error bounds. |
| نوع الوثيقة: | Working Paper |
| الوصول الحر: | http://arxiv.org/abs/2312.08335Test |
| رقم الانضمام: | edsarx.2312.08335 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |